Japenese Restaurant Visitor Exploratory

R & Python

1 Introduction

This is an extensive Exploratory Data Analysis for the Recruit Restaurant Visitor Forecasting competition with the powers of tidy R and ggplot2. Also We tried to translate the main R code to Python.

The aim of this challenge is to predict the future numbers of restaurant visitors. This makes it a Time Series Forecasting problem. The data was collected from Japanese restaurants. As we will see, the data set is small and easily accessible without requiring much memory or computing power. Therefore, this competition is particularly suited for beginners.

The data comes in the shape of 8 relational files which are derived from two separate Japanese websites that collect user information: “Hot Pepper Gourmet (hpg): similar to Yelp” (search and reserve) and “AirREGI / Restaurant Board (air): similar to Square” (reservation control and cash register). The training data is based on the time range of Jan 2016 - most of Apr 2017, while the test set includes the last week of Apr plus May 2017. The test data “intentionally spans a holiday week in Japan called the ‘Golden Week.’ The data description further notes that:”There are days in the test set where the restaurant were closed and had no visitors. These are ignored in scoring. The training set omits days where the restaurants were closed.”

Those are the individual files:

• air_visit_data.csv: historical visit data for the air restaurants. This is essentially the main training data set.

• air_reserve.csv / hpg_reserve.csv: reservations made through the air / hpg systems.

• air_store_info.csv / hpg_store_info.csv: details about the air / hpg restaurants including genre and location.

• store_id_relation.csv: connects the air and hpg ids

• date_info.csv: essentially flags the Japanese holidays.

• sample_submission.csv: serves as the test set. The id is formed by combining the air id with the visit date.

Thank you all for the upvotes, critical feedback, and continued support!

2 Preparations

2.1 Set Python and R Envirments and load packages

2.1.1 for R to use python3

# Set python environment and version in RStudio ;-)
reticulate::use_python("/usr/bin/python3.10", required = TRUE)
reticulate::py_config()

## python:         /usr/bin/python3.10
## libpython:      /usr/lib/python3.10/config-3.10-x86_64-linux-gnu/libpython3.10.so
## pythonhome:     //usr://usr
## version:        3.10.12 (main, Jun 11 2023, 05:26:28) [GCC 11.4.0]
## numpy:          /home/kirus/.local/lib/python3.10/site-packages/numpy
## numpy_version:  1.26.0
## 
## NOTE: Python version was forced by use_python() function

# check module availability
#reticulate::py_module_available("numpy")
#reticulate::py_module_available("matplotlib")
#reticulate::py_module_available("seaborn")

2.1.2 Set Language

#Sys.setlocale("LC_ALL","English")
Sys.setenv(LANG = "en_US.UTF-8")
Sys.setenv("LANGUAGE"="En")

import locale
locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

2.1.3 Check R libraries paths

.libPaths()

## [1] "/home/kirus/R/x86_64-pc-linux-gnu-library/4.3"
## [2] "/usr/local/lib/R/site-library"                
## [3] "/usr/lib/R/site-library"                      
## [4] "/usr/lib/R/library"

2.1.4 Check the path of R envirment used by python

import os
print(os.environ['R_HOME'])

## /usr/lib/R

# os.environ['R_HOME'] = "/home/kirus/R/x86_64-pc-linux-gnu-library/4.3"
# print(os.environ['R_HOME'])

• We need to set R libraries path when called by Python.

• Two paths will be used:

  • /usr/lib/R/library for packages installed with root profile during installing R base,

  • /home/kirus/R/x86_64-pc-linux-gnu-library/4.3 for packages installed by user without root profile.

2.1.5 Check which R version and libraries paths used by `rpy2``

import rpy2.rinterface
#rpy2.rinterface.set_initoptions((b'rpy2', b'--no-save', b'--no-restore', b'--quiet'))
from rpy2.robjects.packages import importr

## /home/kirus/.local/lib/python3.10/site-packages/rpy2/rinterface_lib/embedded.py:276: UserWarning: R was initialized outside of rpy2 (R_NilValue != NULL). Trying to use it nevertheless.
##   warnings.warn(msg)
## R was initialized outside of rpy2 (R_NilValue != NULL). Trying to use it nevertheless.

base = importr('base', lib_loc= '/usr/lib/R/library/')
print(base.version)

print(base._libPaths())

2.2 Load libraries

We load a range of libraries for general data wrangling and general visualisation together with more specialised tools.

# general visualisation
library('ggplot2') # visualisation
library('scales') # visualisation
library('grid') # visualisation
library('gridExtra') # visualisation
library('RColorBrewer') # visualisation
library('corrplot') # visualisation

# general data manipulation
library('dplyr') # data manipulation
library('readr') # input/output
library('data.table') # data manipulation
library('DT') # display table
library('tibble') # data wrangling
library('tidyr') # data wrangling
library('stringr') # string manipulation
library('forcats') # factor manipulation

# specific visualisation
library('ggrepel') # visualisation
library('ggridges') # visualisation
library('ggExtra') # visualisation
library('ggforce') # visualisation
library('viridis') # visualisation

# specific data manipulation
library('lazyeval') # data wrangling
library('broom') # data wrangling
library('purrr') # string manipulation

# Date plus forecast
library('lubridate') # date and time
library('timeDate') # date and time
library('tseries') # time series analysis
library('forecast') # time series analysis
library('prophet') # time series analysis

## Error in library("prophet"): there is no package called 'prophet'

library('timetk') # time series analysis

# Maps / geospatial
library('geosphere') # geospatial locations
library('leaflet') # maps
library('leaflet.extras') # maps
library('maps') # maps

library(reticulate) # interface to python

#pip3 install matplotlib
#pip3 install seaborn
#pip3 install scikit-learn
#pip3 install rpy2
# pip install git+https://github.com/h2oai/datatable
# pip install ipywidgets==7.0.1

from rpy2 import robjects
from rpy2.robjects.packages import importr, data
import rpy2.robjects.packages as rpackages
import rpy2.robjects as ro
from rpy2.robjects import pandas2ri
import matplotlib
from matplotlib import pyplot as plt, dates
#import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import seaborn as sns
import locale
from statsmodels.nonparametric.smoothers_lowess import lowess
from matplotlib.gridspec import GridSpec
import matplotlib.dates as mdates
from matplotlib.ticker import FormatStrFormatter
import folium
from folium.plugins import MarkerCluster
locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

from statsmodels.regression.linear_model import OLS
from statsmodels.tools import add_constant
from datetime import timedelta
from pmdarima import auto_arima
from statsmodels.tsa.seasonal import seasonal_decompose

#from IPython.display import display, HTML # displays html tobale in Rmarkdown
#import ipywidgets 
#import qgrid  # display dataframe like DT::datatable in Rmarkdown document
#import datatable as dt
#from sklearn.model_selection import train_test_split
from collections import Counter
from datetime import datetime
from datetime import date
from prophet import Prophet
from prophet.plot import plot
import plotly

2.3 plot iris datasets

iris %>%
ggplot()+
aes(x=Petal.Length,y=Petal.Width,color=Species, alpha=0.8) +
 geom_point()

#datasets::iris

## Load iris from python
#iris = sns.load_dataset('iris')

# load iris from R
datasets = rpackages.importr('datasets', 
            lib_loc= '/usr/lib/R/library/')
iris = data(datasets).fetch('iris')['iris']

# convert R dataframe to pandas df 
# (https://rpy2.github.io/doc/latest/html/generated_rst/pandas.html)
with (ro.default_converter + pandas2ri.converter).context():
  iris = ro.conversion.get_conversion().rpy2py(iris)
  
  
#sns.set_style("darkgrid")
plt.style.use('ggplot')
#fi = sns.FacetGrid(iris, hue ="Species", 
#              height = 6).map(plt.scatter, 
#                              'Petal.Length', 
#                              'Petal.Width').add_legend()

fi=sns.relplot(x="Petal.Length", 
               y="Petal.Width", 
               data=iris, alpha=0.8, 
               hue='Species') 
fi.fig.set_figheight(4)
fi.fig.set_figwidth(8)
plt.show()

2.4 Helper functions

We use the multiplot function, courtesy of R Cookbooks to create multi-panel plots. We also make use of a brief helper function to compute binomial confidence intervals.

# Define multiple plot function
#
# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
# - cols:   Number of columns in layout
# - layout: A matrix specifying the layout. If present, 'cols' is ignored.
#
# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),
# then plot 1 will go in the upper left, 2 will go in the upper right, and
# 3 will go all the way across the bottom.
#
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {

  # Make a list from the ... arguments and plotlist
  plots <- c(list(...), plotlist)

  numPlots = length(plots)

  # If layout is NULL, then use 'cols' to determine layout
  if (is.null(layout)) {
    # Make the panel
    # ncol: Number of columns of plots
    # nrow: Number of rows needed, calculated from # of cols
    layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
                    ncol = cols, nrow = ceiling(numPlots/cols))
  }

 if (numPlots==1) {
    print(plots[[1]])

  } else {
    # Set up the page
    grid.newpage()
    pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))

    # Make each plot, in the correct location
    for (i in 1:numPlots) {
      # Get the i,j matrix positions of the regions that contain this subplot
      matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))

      print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
                                      layout.pos.col = matchidx$col))
    }
  }
}

We use matplotlib to create subplots. The function multiplot now works with *args to accept an arbitrary number of plots, and the cols argument determines the number of columns in the layout. If layout is not provided, it is calculated from cols and the number of plots.

The example at the end demonstrates how to use the multiplot function with two plots (y1 and y2) arranged in two columns.

import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec

def multiplot(*args, plotlist=None, file=None, cols=1, layout=None):
    plots = list(args) + (plotlist if plotlist else [])
    num_plots = len(plots)
    
    if layout is None:
        rows = (num_plots - 1) // cols + 1
        layout = [(i // cols, i % cols) for i in range(num_plots)]

    if num_plots == 1:
        plt.subplot2grid((rows, cols), (0, 0))
        plt.plot(plots[0])
        
    else:
        fig = plt.figure()
        gs = GridSpec(rows, cols)

        for i, plot in enumerate(plots):
            ax = fig.add_subplot(gs[layout[i]])
            ax.plot(plot)

    if file:
        plt.savefig(file)
    else:
        plt.show()

# Example usage
#import numpy as np

#x = np.linspace(0, 10, 100)
#y1 = np.sin(x)
#y2 = np.cos(x)

#multiplot(y1, y2, cols=2)

An other version using add_gridspec to create a layout for multiple plots:

def multiplot(*args, plotlist=None, file=None, cols=1, layout=None):
    plots = list(args) + (plotlist if plotlist else [])
    num_plots = len(plots)
    
    if layout is None:
        rows = (num_plots - 1) // cols + 1

    fig = plt.figure()

    if num_plots == 1:
        plt.subplot2grid((rows, cols), (0, 0), colspan=cols)
        plt.plot(plots[0])
        
    else:
        gs = GridSpec(rows, cols)

        for i, plot in enumerate(plots):
            ax = fig.add_subplot(gs[i // cols, i % cols])
            ax.plot(plot)

    if file:
        plt.savefig(file)
    else:
        plt.show()

2.5 Load Data

air_visits <- data.table::fread(str_c("data/air_visit_data.csv"))
air_reserve <- data.table::fread(str_c('data/air_reserve.csv'))
air_store <- data.table::fread(str_c('data/air_store_info.csv'))
holidays <- data.table::fread(str_c('data/date_info.csv'))
hpg_reserve <- data.table::fread(str_c('data/hpg_reserve.csv'))
hpg_store <- data.table::fread(str_c('data/hpg_store_info.csv'))
store_ids <- data.table::fread(str_c('data/store_id_relation.csv'))
test <- data.table::fread(str_c('data/sample_submission.csv'))

In this Python code, we use the pandas library to read the CSV files. Each read_csv function call reads a CSV file into a DataFrame. The variable names (air_visit, air_reserve, etc.) will be DataFrames that you can use for data manipulation and analysis.

air_visits = pd.read_csv("data/air_visit_data.csv")
air_reserve = pd.read_csv("data/air_reserve.csv")
air_store = pd.read_csv("data/air_store_info.csv")
holidays = pd.read_csv("data/date_info.csv")
hpg_reserve = pd.read_csv("data/hpg_reserve.csv")
hpg_store = pd.read_csv("data/hpg_store_info.csv")
store_ids = pd.read_csv("data/store_id_relation.csv")
test = pd.read_csv("data/sample_submission.csv")

3 Overview: File structure and content

As a first step let’s have an overview of the data sets.

3.1 Air visits

air_visits %>%
  head(10) %>%
  DT::datatable()

We find that this file contains the visitors numbers for each visit_date and air_store_id. The date feature should be transformed into a time-series format. There are 829 different stores, which is a small data set:

air_visits %>%
  distinct(air_store_id) %>%
  nrow()

## [1] 829

qgrid and ipywidgets verions are not compatible and have a issue to render html table like DT::datatable().

#air_visits = pd.DataFrame(air_visits)

# Show the DataFrame using qgrid in Python
#qgrid_widget = qgrid.show_grid(air_visits, show_toolbar=True)
#qgrid_widget.head(10)

#html = air_visits.head(10).to_html()
#display(HTML(html))
#print(html)
air_visits.head(10)

##            air_store_id  visit_date  visitors
## 0  air_ba937bf13d40fb24  2016-01-13        25
## 1  air_ba937bf13d40fb24  2016-01-14        32
## 2  air_ba937bf13d40fb24  2016-01-15        29
## 3  air_ba937bf13d40fb24  2016-01-16        22
## 4  air_ba937bf13d40fb24  2016-01-18         6
## 5  air_ba937bf13d40fb24  2016-01-19         9
## 6  air_ba937bf13d40fb24  2016-01-20        31
## 7  air_ba937bf13d40fb24  2016-01-21        21
## 8  air_ba937bf13d40fb24  2016-01-22        18
## 9  air_ba937bf13d40fb24  2016-01-23        26

air_visits['air_store_id'].nunique()

## 829

3.2 Air Reserve

air_reserve %>%
  head(10) %>%
  DT::datatable()

We find that the air reservations include the date and time of the reservation, as well as those of the visit. We have reservation numbers for 314 air stores:

air_reserve %>% distinct(air_store_id) %>% nrow()

## [1] 314

air_reserve.head(10)

##            air_store_id  ... reserve_visitors
## 0  air_877f79706adbfb06  ...                1
## 1  air_db4b38ebe7a7ceff  ...                3
## 2  air_db4b38ebe7a7ceff  ...                6
## 3  air_877f79706adbfb06  ...                2
## 4  air_db80363d35f10926  ...                5
## 5  air_db80363d35f10926  ...                2
## 6  air_db80363d35f10926  ...                4
## 7  air_3bb99a1fe0583897  ...                2
## 8  air_3bb99a1fe0583897  ...                2
## 9  air_2b8b29ddfd35018e  ...                2
## 
## [10 rows x 4 columns]

air_reserve['air_store_id'].nunique()

## 314

3.3 HPG Reserve

  hpg_reserve %>%
  head(10) %>%
  DT::datatable()

The hpg reservations file follows the same structure as the corresponding air file. We have reservation numbers for 13325 hpg stores:

hpg_reserve %>% distinct(hpg_store_id) %>% nrow()

## [1] 13325

hpg_reserve.head(10)

##            hpg_store_id  ... reserve_visitors
## 0  hpg_c63f6f42e088e50f  ...                1
## 1  hpg_dac72789163a3f47  ...                3
## 2  hpg_c8e24dcf51ca1eb5  ...                2
## 3  hpg_24bb207e5fd49d4a  ...                5
## 4  hpg_25291c542ebb3bc2  ...               13
## 5  hpg_28bdf7a336ec6a7b  ...                2
## 6  hpg_2a01a042bca04ad9  ...                2
## 7  hpg_2a84dd9f4c140b82  ...                2
## 8  hpg_2ad179871696901f  ...                2
## 9  hpg_2c1d989eedb0ff83  ...                6
## 
## [10 rows x 4 columns]

hpg_reserve['hpg_store_id'].nunique()

## 13325

3.4 Air Store

air_store %>%
  head(10) %>%
  datatable()

We find that the air_store info includes the name of the particular cuisine along with the name of the area.

air_store.head(10)

##            air_store_id  air_genre_name  ...   latitude   longitude
## 0  air_0f0cdeee6c9bf3d7  Italian/French  ...  34.695124  135.197853
## 1  air_7cc17a324ae5c7dc  Italian/French  ...  34.695124  135.197853
## 2  air_fee8dcf4d619598e  Italian/French  ...  34.695124  135.197853
## 3  air_a17f0778617c76e2  Italian/French  ...  34.695124  135.197853
## 4  air_83db5aff8f50478e  Italian/French  ...  35.658068  139.751599
## 5  air_99c3eae84130c1cb  Italian/French  ...  35.658068  139.751599
## 6  air_f183a514cb8ff4fa  Italian/French  ...  35.658068  139.751599
## 7  air_6b9fa44a9cf504a1  Italian/French  ...  35.658068  139.751599
## 8  air_0919d54f0c9a24b8  Italian/French  ...  35.658068  139.751599
## 9  air_2c6c79d597e48096  Italian/French  ...  35.658068  139.751599
## 
## [10 rows x 5 columns]

3.5 HPG Store

hpg_store %>%
  head(10) %>%
  datatable()

Again, the hpg_store info follows the same structure as the air info. Here the genre_name includes the word style. It’s worth checking whether the same is true for the air data or whether it just refers to the specific “Japanese style”. There are 4690 different hpg_store_ids, which are significantly fewer than we have reservation data for.

hpg_store.head(10)

##            hpg_store_id  hpg_genre_name  ...   latitude   longitude
## 0  hpg_6622b62385aec8bf  Japanese style  ...  35.643675  139.668221
## 1  hpg_e9e068dd49c5fa00  Japanese style  ...  35.643675  139.668221
## 2  hpg_2976f7acb4b3a3bc  Japanese style  ...  35.643675  139.668221
## 3  hpg_e51a522e098f024c  Japanese style  ...  35.643675  139.668221
## 4  hpg_e3d0e1519894f275  Japanese style  ...  35.643675  139.668221
## 5  hpg_530cd91db13b938e  Japanese style  ...  35.643675  139.668221
## 6  hpg_02457b318e186fa4  Japanese style  ...  35.643675  139.668221
## 7  hpg_0cb3c2c490020a29  Japanese style  ...  35.643675  139.668221
## 8  hpg_3efe9b08c887fe9a  Japanese style  ...  35.643675  139.668221
## 9  hpg_765e8d3ba261dc1c  Japanese style  ...  35.643675  139.668221
## 
## [10 rows x 5 columns]

3.6 Holidays

holidays %>%
  head(10) %>%
  datatable()

We called the date_info file holidays, because that’s essentially the information it contains. Holidays are encoded as binary flags in integer format. This should become a logical binary feature for exploration purposes.

holidays.head(10)

##   calendar_date day_of_week  holiday_flg
## 0    2016-01-01      Friday            1
## 1    2016-01-02    Saturday            1
## 2    2016-01-03      Sunday            1
## 3    2016-01-04      Monday            0
## 4    2016-01-05     Tuesday            0
## 5    2016-01-06   Wednesday            0
## 6    2016-01-07    Thursday            0
## 7    2016-01-08      Friday            0
## 8    2016-01-09    Saturday            0
## 9    2016-01-10      Sunday            0

3.7 Store IDs

store_ids %>%
  head(10) %>%
  datatable()

This is a relational file that connects the air and hpg ids. There are only 150 pairs, which is less than 20% of all air stores.

store_ids.head(10)

##            air_store_id          hpg_store_id
## 0  air_63b13c56b7201bd9  hpg_4bc649e72e2a239a
## 1  air_a24bf50c3e90d583  hpg_c34b496d0305a809
## 2  air_c7f78b4f3cba33ff  hpg_cd8ae0d9bbd58ff9
## 3  air_947eb2cae4f3e8f2  hpg_de24ea49dc25d6b8
## 4  air_965b2e0cf4119003  hpg_653238a84804d8e7
## 5  air_a38f25e3399d1b25  hpg_50378da9ffb9b6cd
## 6  air_3c938075889fc059  hpg_349b1b92f98b175e
## 7  air_68301bcb11e2f389  hpg_2c09f3abb2220659
## 8  air_5f6fa1b897fe80d5  hpg_40aff6385800ebb1
## 9  air_00a91d42b08b08d9  hpg_fbe603376b5980fc

3.8 Test data

test %>%
  head(10) %>%
  datatable()

As noted in the data description, the id of the final submission file is a concatenation of the air_id and the date.

test.head(10)

##                                 id  visitors
## 0  air_00a91d42b08b08d9_2017-04-23         0
## 1  air_00a91d42b08b08d9_2017-04-24         0
## 2  air_00a91d42b08b08d9_2017-04-25         0
## 3  air_00a91d42b08b08d9_2017-04-26         0
## 4  air_00a91d42b08b08d9_2017-04-27         0
## 5  air_00a91d42b08b08d9_2017-04-28         0
## 6  air_00a91d42b08b08d9_2017-04-29         0
## 7  air_00a91d42b08b08d9_2017-04-30         0
## 8  air_00a91d42b08b08d9_2017-05-01         0
## 9  air_00a91d42b08b08d9_2017-05-02         0

3.9 Missing values

sum(is.na(air_visits))

## [1] 0

sum(is.na(air_reserve))

## [1] 0

sum(is.na(hpg_reserve))

## [1] 0

sum(is.na(air_store))

## [1] 0

sum(is.na(hpg_store))

## [1] 0

sum(is.na(holidays))

## [1] 0

sum(is.na(store_ids))

## [1] 0

sum(is.na(test))

## [1] 0

There are no missing values in our data. Excellent.

In Python, you can use the isna() method from the pandas library to check for missing values in a DataFrame, and then use sum() to count them. Here’s the equivalent code:

air_visits.isna().sum().sum()

## 0

air_reserve.isna().sum().sum()

## 0

hpg_reserve.isna().sum().sum()

## 0

air_store.isna().sum().sum()

## 0

hpg_store.isna().sum().sum()

## 0

holidays.isna().sum().sum()

## 0

test.isna().sum().sum()

## 0

• test.isna() returns a DataFrame of the same shape as test with True where the original DataFrame has missing values, and False otherwise.

• .sum() is used twice. The first sum() computes the count of missing values for each column, and the second sum() adds up those counts to get the total number of missing values in the entire DataFrame.

• The final result, missing_values_count, will be the equivalent of sum(is.na(test)) in R.

3.10 Reformating feature

We change the formatting of the date/time features and also reformat a few features to logical and factor variables for exploration purposes.

air_visits <- air_visits %>%
  mutate(visit_date = ymd(visit_date))

air_reserve <- air_reserve %>%
  mutate(visit_datetime = as.POSIXct(visit_datetime,format="%Y-%m-%dT%H:%MZ"), #ymd_hms(visit_datetime),
         reserve_datetime = as.POSIXct(reserve_datetime,format="%Y-%m-%dT%H:%MZ")) #ymd_hms(reserve_datetime)

hpg_reserve <- hpg_reserve %>%
  mutate(visit_datetime = as.POSIXct(visit_datetime,format="%Y-%m-%dT%H:%MZ"),
         reserve_datetime = as.POSIXct(reserve_datetime,format="%Y-%m-%dT%H:%MZ"))

air_store <- air_store %>%
  mutate(air_genre_name = as.factor(air_genre_name),
         air_area_name = as.factor(air_area_name))

hpg_store <- hpg_store %>%
  mutate(hpg_genre_name = as.factor(hpg_genre_name),
         hpg_area_name = as.factor(hpg_area_name))

holidays <- holidays %>%
  mutate(holiday_flg = as.logical(holiday_flg),
         date = ymd(calendar_date),
         calendar_date = as.character(calendar_date))

# Convert visit_date column to datetime format
air_visits['visit_date'] = pd.to_datetime(air_visits['visit_date'])

# Convert visit_datetime and reserve_datetime columns to datetime format
air_reserve['visit_datetime'] = pd.to_datetime(air_reserve['visit_datetime'])
air_reserve['reserve_datetime'] = pd.to_datetime(air_reserve['reserve_datetime'])

hpg_reserve['visit_datetime'] = pd.to_datetime(hpg_reserve['visit_datetime'])
hpg_reserve['reserve_datetime'] = pd.to_datetime(hpg_reserve['reserve_datetime'])

# Convert categorical columns to factors (categorical variables in pandas)
air_store['air_genre_name'] = air_store['air_genre_name'].astype('category')
air_store['air_area_name'] = air_store['air_area_name'].astype('category')

hpg_store['hpg_genre_name'] = hpg_store['hpg_genre_name'].astype('category')
hpg_store['hpg_area_name'] = hpg_store['hpg_area_name'].astype('category')

# Convert holiday_flg to boolean, date to datetime, and calendar_date to string
holidays['holiday_flg'] = holidays['holiday_flg'].astype(bool)
holidays['date'] = pd.to_datetime(holidays['calendar_date'])
holidays['calendar_date'] = holidays['calendar_date'].astype(str)

4 Individual feature

Here we have a first look at the distributions of the feature in our individual data files before combining them for a more detailed analysis. This inital visualisation will be the foundation on which we build our analysis.

4.1 Air Visits

We start with the number of visits to the air restaurants. Here we plot the total number of visitors per day over the full training time range together with the median visitors per day of the week and month of the year:

Sys.setenv(LANG = "en_US.UTF-8")

p1 <- air_visits %>%
  group_by(visit_date) %>%
  summarise(all_visitors = sum(visitors)) %>%
  ggplot(aes(visit_date,all_visitors)) +
  geom_line(col = "blue") +
  labs(y = "All visitors", x = "Date")

p2 <- air_visits %>%
  ggplot(aes(visitors)) +
  geom_vline(xintercept = 20, color = "orange") +
  geom_histogram(fill = "blue", bins = 30) +
  scale_x_log10()

p3 <- air_visits %>%
  mutate(wday = wday(visit_date, label = TRUE, week_start = 1)) %>%
  group_by(wday) %>%
  summarise(visits = median(visitors)) %>%
  ggplot(aes(wday, visits, fill = wday)) +
  geom_col() +
  theme(legend.position = "none", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9)) +
  labs(x = "Day of the week", y = "Median visitors") +
  scale_fill_hue()
  
p4 <- air_visits %>%
  mutate(month = month(visit_date, label = TRUE)) %>%
  group_by(month) %>%
  summarise(visits = median(visitors)) %>%
  ggplot(aes(month, visits, fill = month)) +
  geom_col() +
  theme(legend.position = "none", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9)) +
  labs(x = "Month", y = "Median visitors")

layout <- matrix(c(1,1,1,1,2,3,4,4),2,4,byrow=TRUE)
multiplot(p1, p2, p3, p4, layout=layout)

We find: * There is an interesting long-term step structure in the overall time series. This might be related to new restaurants being added to the data base. In addition, we already see a periodic pattern that most likely corresponds to a weekly cycle.

• The number of guests per visit per restaurant per day peaks at around 20 (the orange line). The distribution extends up to 100 and, in rare cases, beyond.

• Friday and the weekend appear to be the most popular days; which is to be expected. Monday and Tuesday have the lowest numbers of average visitors.

• Also during the year there is a certain amount of variation. Dec appears to be the most popular month for restaurant visits. The period of Mar - May is consistently busy.

We will be forecasting for the last week of April plus May 2017, so let’s look at this time range in our 2016 training data:

air_visits %>%
  filter(visit_date > ymd("2016-04-15") & visit_date < ymd("2016-06-15")) %>%
  group_by(visit_date) %>%
  summarise(all_visitors = sum(visitors)) %>%
  ggplot(aes(visit_date,all_visitors)) +
  geom_line() +
  geom_smooth(method = "loess", color = "blue", span = 1/7) +
  labs(y = "All visitors", x = "Date")

## `geom_smooth()` using formula = 'y ~ x'

Here, the black line is the date and the blue line corresponds to a smoothing fit with a corresponding grey confidence area. We see again the weekly period and also the impact of the aforementioned Golden Week, which in 2016 happened between Apr 29 and May 5.

Seaborn doesn’t have a direct equivalent to the geom_smooth function with the loess method. However, we can achieve a similar effect using the seaborn.lineplot function combined with a lowess smoother from the statsmodels library.

locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

# Set the language to English
#plt.rcParams['axes.formatter.use_locale'] = False
#plt.rcParams['pgf.rcfonts'] = False
#plt.rcParams['pdf.fonttype'] = 42

p1_data = air_visits.groupby('visit_date', observed=True)['visitors'].sum().reset_index()

p3_data = air_visits.assign(wday=air_visits['visit_date'].dt.day_name()).groupby('wday')['visitors'].median().reset_index()

p4_data = air_visits.assign(month=air_visits['visit_date'].dt.strftime('%b')).groupby('month')['visitors'].median().reset_index()


plt.style.use('ggplot')
fig = plt.figure(figsize=(11, 6))
gs = fig.add_gridspec(2, 3)

# First row
ax1 = fig.add_subplot(gs[0, :])
sns.lineplot(data=p1_data, x='visit_date', y='visitors', color='blue', ax=ax1)
ax1.set_xlabel('All visitors')
ax1.set_ylabel('Date')

# Second row
ax2 = fig.add_subplot(gs[1, 0])
plt.axvline(x=20, color='orange')
plt.xscale('log')
sns.histplot(data=air_visits, x='visitors', bins=30, color='blue', kde=True, ax=ax2)

ax3 = fig.add_subplot(gs[1, 1])
order = [ "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
ax3.set_xticklabels( ('Mon', 'Tue','Wed', 'Thur', 'Fri', 'Sat', 'Sun') )
p3 = sns.barplot(data=p3_data, x='wday', y='visitors', hue='wday', 
                  legend=False, ax=ax3, order=order) #palette='viridis',
p3 = plt.xticks(rotation=45)
#ax3.set_xticklabels(ax3.get_xticklabels(), rotation=45)
ax3.set_xlabel('Days')

ax4 = fig.add_subplot(gs[1, 2])
order = [ "Jan", "Feb", "Mar", "Apr", "May", "Jun","Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
p4 = sns.barplot(data=p4_data, x='month', y='visitors', hue='month',
         legend=False, ax=ax4, order=order, palette='viridis')
p4 = plt.xticks(rotation=45)
#ax4.set_xticklabels(ax4.get_xticklabels(), rotation=45)
ax4.set_xlabel('Months')

plt.tight_layout()
plt.show()

• In this code, we use add_gridspec to create a 2x3 grid of subplots.

• Then, we manually add subplots to specific positions using add_subplot.

• This way, you have full control over the layout of the plots.

from statsmodels.nonparametric.smoothers_lowess import lowess
import matplotlib.dates as mdates
#locale.setlocale(locale.LC_ALL,'en_US.utf8')

plt.style.use('ggplot')

# Assuming air_visits is your DataFrame
subset_data = air_visits[(air_visits['visit_date'] > '2016-04-15') &
                        (air_visits['visit_date'] < '2016-06-15')]
# Calculate the total visitors for each visit_date
agg_data = subset_data.groupby('visit_date')['visitors'].sum().reset_index()
#agg_data.visit_date = agg_data.visit_date.dt.strftime('%d %b')

# build the figure
fig, ax = plt.subplots()

# Scatter plot of the data
p = sns.lineplot(data = agg_data, x='visit_date', y='visitors',
                 color='black', label='Data')
#p= sns.regplot(data=agg_data, x='visit_date', y='visitors',
#                color='black', lowess=True, ax=plt.gca())

# set dates format
p = ax.set(xticklabels = agg_data['visit_date'].dt.strftime('%d %b'))

## <string>:5: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.

p = plt.fill_between(agg_data.visit_date, agg_data.visitors*0.8,
                        agg_data.visitors*1.2, 
                        alpha=0.25, label='LOWESS uncertainty',
                        color = "grey")


# put the labels at 45deg since they tend to be too long
#p = plt.xticks(rotation=45)
fig.autofmt_xdate() 

# # Ensure that the x.axis text is spacieux 
p = ax.xaxis.set_major_locator(mdates.AutoDateLocator())

## Calculate the lowess smoothed line
smoothed = lowess(agg_data['visitors'], 
           agg_data['visit_date'].astype('datetime64[s]'),  frac=1/7)
## Plot the smoothed line
p = plt.plot(agg_data['visit_date'], smoothed[:, 1],
    color='blue', label='Lowess Smoother')

# Set labels and legend
p = plt.xlabel('Date')
p = plt.ylabel('All visitors')
plt.legend("")

# Show the plot
plt.show(p)

4.2 Air Reservations

Let’s see how our reservations data compares to the actual visitor numbers. We start with the air restaurants and visualise their visitor volume through reservations for each day, alongside the hours of these visits and the time between making a reservation and visiting the restaurant:

foo <- air_reserve %>%
  mutate(reserve_date = date(reserve_datetime),
         reserve_hour = hour(reserve_datetime),
         reserve_wday = wday(reserve_datetime, label = TRUE, week_start = 1),
         visit_date = date(visit_datetime),
         visit_hour = hour(visit_datetime),
         visit_wday = wday(visit_datetime, label = TRUE, week_start = 1),
         diff_hour = time_length(visit_datetime - reserve_datetime, unit = "hour"),
         diff_day = time_length(visit_datetime - reserve_datetime, unit = "day")
         )

p1 <- foo %>%
  group_by(visit_date) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(visit_date, all_visitors)) +
  geom_line() +
  labs(x = "Air visit date")

p2 <- foo %>%
  group_by(visit_hour) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(visit_hour, all_visitors)) +
  geom_col(fill = "blue")

p3 <- foo %>%
  filter(diff_hour < 24*5) %>%
  group_by(diff_hour) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(diff_hour, all_visitors)) +
  geom_col(fill = "blue") +
  labs(x = "Time from reservation to visit (hours)")

layout <- matrix(c(1,1,2,3),2,2, byrow=TRUE)
multiplot(p1, p2, p3, layout=layout)

# Assuming 'air_reserve' is your DataFrame
foo = air_reserve.copy()
foo['reserve_date'] = foo['reserve_datetime'].dt.date
foo['reserve_hour'] = foo['reserve_datetime'].dt.hour
foo['reserve_wday'] = foo['reserve_datetime'].dt.day_name()
foo['visit_date'] = foo['visit_datetime'].dt.date
foo['visit_hour'] = foo['visit_datetime'].dt.hour
foo['visit_wday'] = foo['visit_datetime'].dt.day_name()
foo['diff_hour'] = (foo['visit_datetime'] - foo['reserve_datetime']).dt.total_seconds() / 3600
foo['diff_day'] = (foo['visit_datetime'] - foo['reserve_datetime']).dt.days

p1 = foo.groupby('visit_date')['reserve_visitors'].sum().reset_index()
p2 = foo.groupby('visit_hour')['reserve_visitors'].sum().reset_index()
p3 = foo[foo['diff_hour'] < 24*5].groupby('diff_hour')['reserve_visitors'].sum().reset_index()

# Multiplot layout
fig = plt.figure(figsize=(9, 5))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

ax1 = fig.add_subplot(gs[0, :])
ax2 = fig.add_subplot(gs[1, 0])
ax3 = fig.add_subplot(gs[1, 1])

p1.plot(x='visit_date', y='reserve_visitors', kind='line', ax=ax1, color = 'black')
p1= ax1.set_xlabel('air visit date')
p1= plt.legend("")

p2.plot(x='visit_hour', y='reserve_visitors', kind='bar', color='blue', ax=ax2)
p2= ax2.set_xticklabels(ax2.get_xticklabels(), rotation=0)
p2= ax2.xaxis.set_major_locator(mdates.AutoDateLocator())
p2= plt.legend("")

p3.plot(x='diff_hour', y='reserve_visitors', kind='bar', color='blue', ax=ax3)
p3= ax3.set_xlabel('Time from reservation to visit (hours)')
p3= ax3.set_xticklabels(ax3.get_xticklabels(), rotation=0)
p3= ax3.xaxis.set_major_locator(mdates.AutoDateLocator())
p3= ax3.xaxis.set_major_formatter(FormatStrFormatter('%.0f'))
p3= plt.legend("")

plt.tight_layout()
plt.show()

4.3 HPG Reservations

In the same style as above, here are the hpg reservations:

foo <- hpg_reserve %>%
  mutate(reserve_date = date(reserve_datetime),
         reserve_hour = hour(reserve_datetime),
         visit_date = date(visit_datetime),
         visit_hour = hour(visit_datetime),
         diff_hour = time_length(visit_datetime - reserve_datetime, unit = "hour"),
         diff_day = time_length(visit_datetime - reserve_datetime, unit = "day")
         )

p1 <- foo %>%
  group_by(visit_date) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(visit_date, all_visitors)) +
  geom_line() +
  labs(x = "HPG visit date")

p2 <- foo %>%
  group_by(visit_hour) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(visit_hour, all_visitors)) +
  geom_col(fill = "red")

p3 <- foo %>%
  filter(diff_hour < 24*5) %>%
  group_by(diff_hour) %>%
  summarise(all_visitors = sum(reserve_visitors)) %>%
  ggplot(aes(diff_hour, all_visitors)) +
  geom_col(fill = "red") +
  labs(x = "Time from reservation to visit (hours)")

layout <- matrix(c(1,1,2,3),2,2,byrow=TRUE)
multiplot(p1, p2, p3, layout=layout)

We find:

• Here the visits after reservation follow a more orderly pattern, with a clear spike in Dec 2016. As above for the air data, we also see reservation visits dropping off as we get closer to the end of the time frame.

• Again, most reservations are for dinner, and we see another nice 24-hour pattern for making these reservations. It’s worth noting that here the last few hours before the visit don’t see more volume than the 24 or 48 hours before. This is in stark constrast to the air data.

foo = hpg_reserve.copy()
foo['reserve_date'] = foo['reserve_datetime'].dt.date
foo['reserve_hour'] = foo['reserve_datetime'].dt.hour
foo['visit_date'] = foo['visit_datetime'].dt.date
foo['visit_hour'] = foo['visit_datetime'].dt.hour
foo['diff_hour'] = (foo['visit_datetime'] - foo['reserve_datetime']).dt.total_seconds() / 3600
foo['diff_day'] = (foo['visit_datetime'] - foo['reserve_datetime']).dt.days

p1 = foo.groupby('visit_date')['reserve_visitors'].sum().reset_index()
p2 = foo.groupby('visit_hour')['reserve_visitors'].sum().reset_index()
p3 = foo[foo['diff_hour'] < 24*5].groupby('diff_hour')['reserve_visitors'].sum().reset_index()

# Multiplot layout
fig = plt.figure(figsize=(9, 5))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

ax1 = fig.add_subplot(gs[0, :])
ax2 = fig.add_subplot(gs[1, 0])
ax3 = fig.add_subplot(gs[1, 1])

p1.plot(x='visit_date', y='reserve_visitors', kind='line', color='black', ax=ax1)
p1= ax1.set_xlabel('HPG visit date')
#p1= ax1.set_xticklabels(ax1.get_xticklabels(), rotation=45)
p1= ax1.xaxis.set_major_locator(mdates.AutoDateLocator())
p1= plt.legend("")

p2.plot(x='visit_hour', y='reserve_visitors', kind='bar', color='red', ax=ax2)
p2= ax2.set_xticklabels(ax2.get_xticklabels(), rotation=0)
p2= ax2.xaxis.set_major_locator(mdates.AutoDateLocator())
p2= plt.legend("")

p3.plot(x='diff_hour', y='reserve_visitors', kind='bar', color='red', ax=ax3)
p3= ax3.set_xlabel('Time from reservation to visit (hours)')
p3= ax3.set_xticklabels(ax3.get_xticklabels(), rotation=0)
p3= ax3.xaxis.set_major_locator(mdates.AutoDateLocator())
p3= ax3.xaxis.set_major_formatter(FormatStrFormatter('%.0f'))
p3= plt.legend("")


plt.tight_layout()
plt.show()

4.4 Air Store

After visualising the temporal aspects, let’s now look at the spatial information. Note, that according to the data description the latitude and longitude are the latitude and longitude of the area to which the store belongs. This is meant to discourage us from identifying specific restaurants. I would be surprised if nobody tried anyway, though.

This is a fully interactive and zoomable map of all the air restaurants. Click on the clusters to break them up into smaller clusters and ultimately into the individual restaurants, which are labelled by their genre. The map nicely visualises the fact that many restaurants share common coordinates, since those coordinates refer to the area of the restaurant. Click on the single markers to see their air_store_id. The map is powered by the leaflet package, which includes a variety of cool tools for interactive maps. Have fun exploring!

leaflet(air_store) %>%
  addTiles() %>%
  addProviderTiles("CartoDB.Positron") %>%
  addMarkers(~longitude, ~latitude,
             popup = ~air_store_id, label = ~air_genre_name,
             clusterOptions = markerClusterOptions())

Next, we plot the numbers of different types of cuisine (or air_genre_names) alongside the areas with the most air restaurants:

p1 <- air_store %>%
  group_by(air_genre_name) %>%
  count() %>%
  ggplot(aes(reorder(air_genre_name, n, FUN = min), n, fill = air_genre_name)) +
  geom_col() +
  coord_flip() +
  theme(legend.position = "none") +
  labs(x = "Type of cuisine (air_genre_name)", y = "Number of air restaurants")
  
p2 <- air_store %>%
  group_by(air_area_name) %>%
  count() %>%
  ungroup() %>%
  top_n(15,n) %>%
  ggplot(aes(reorder(air_area_name, n, FUN = min) ,n, fill = air_area_name)) +
  geom_col() +
  theme(legend.position = "none") +
  coord_flip() +
  labs(x = "Top 15 areas (air_area_name)", y = "Number of air restaurants")

layout <- matrix(c(1,2),2,1,byrow=TRUE)
multiplot(p1, p2, layout=layout)

We find:

• There are lots of Izakaya gastropubs in our data, followed by Cafe’s. We don’t have many Karaoke places in the air data set and also only a few that describe themselves as generically International or Asian. I have to admit, I’m kind of intrigued by creative cuisine.

• Fukuoka has the largest number of air restaurants per area, followed by many Tokyo areas.

In Python, you can achieve a similar map using the folium library.

import warnings
warnings.filterwarnings('ignore')

# Create a map centered at a specific location
m = folium.Map(location=[air_store['latitude'].median(),
               air_store['longitude'].median()],
               zoom_start=7, width=1500, height=800)

# Add tiles (you can choose different providers)
folium.TileLayer(tiles='CartoDB positron').add_to(m)

## <folium.raster_layers.TileLayer object at 0x7f7ef38dc8e0>

# Create a MarkerCluster object
marker_cluster = MarkerCluster().add_to(m)

## Add markers from the air_store dataset
# for index, row in air_store.iterrows():
#     folium.Marker(location=[row['latitude'], row['longitude']],
#                   popup=row['air_store_id'],
#                   icon=None,
#                   tooltip=row['air_genre_name']).add_to(marker_cluster)

# Define a function to add markers
def add_marker(row):
    folium.Marker(location=[row['latitude'], row['longitude']],
                  popup=row['air_store_id'],
                  icon=None,
                  tooltip=row['air_genre_name']).add_to(marker_cluster)

# Apply the function to each row of the DataFrame
air_store.apply(add_marker, axis=1)

## 0      None
## 1      None
## 2      None
## 3      None
## 4      None
##        ... 
## 824    None
## 825    None
## 826    None
## 827    None
## 828    None
## Length: 829, dtype: object

# Display the map
m

Make this Notebook Trusted to load map: File -> Trust Notebook

p1_data = air_store['air_genre_name'].value_counts().reset_index()
p1_data.columns = ['air_genre_name', 'count']
p1_data = p1_data.sort_values(by=['count'], ascending=False).reset_index(drop=True)

p2_data = air_store['air_area_name'].value_counts().nlargest(15).reset_index()
p2_data.columns = ['air_area_name', 'count']
p2_data = p2_data.sort_values(['count'], ascending=False).reset_index(drop=True)


# Multiplot layout
fig = plt.figure(figsize=(10, 5))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

ax1 = fig.add_subplot(gs[0, :])
ax2 = fig.add_subplot(gs[1, :])

# Plot 1
p1= sns.barplot(data=p1_data, x='count', y='air_genre_name', order=p1_data['air_genre_name'],
                palette='dark', ax=ax1, legend=False)
p1= ax1.set_xlabel('Number of air restaurants')
p1= ax1.set_ylabel("Type of cuisine")
#p1= ax1.set_title("Number of air restaurants by cuisine type")
#p1= ax1.set_xticklabels(ax1.get_xticklabels(), rotation=0)
#p1= ax1.yaxis.set_major_locator(mdates.AutoDateLocator())
#p1= plt.legend("")

# Plot 2
p2= sns.barplot(data=p2_data, x='count', y='air_area_name', order=p2_data['air_area_name'],
                palette='bright', ax=ax2, legend=False, width=0.8)
p2= ax2.set_xlabel("Number of air restaurants")
p2= ax2.set_ylabel("Top 15 areas")
#p2= ax2.set_title("Top 15 areas with most air restaurants")
#p2= ax2.set_xticklabels(ax2.get_xticklabels(), rotation=0)
#p2= ax2.yaxis.set_major_locator(mdates.AutoDateLocator())
p2= plt.legend("")
plt.tight_layout()
plt.show()

4.5 HPG Store

In the same way as for the air stores above, we also create an interactive map for the different hpg restaurants:

leaflet(hpg_store) %>%
  addTiles() %>%
  addProviderTiles("CartoDB.Positron") %>%
  addMarkers(~longitude, ~latitude,
             popup = ~hpg_store_id, label = ~hpg_genre_name,
              clusterOptions = markerClusterOptions())

Here is the breakdown of genre and area for the hpg restaurants

p1 <- hpg_store %>%
  group_by(hpg_genre_name) %>%
  count() %>%
  ggplot(aes(reorder(hpg_genre_name, n, FUN = min), n, fill = hpg_genre_name)) +
  geom_col() +
  coord_flip() +
  theme(legend.position = "none") +
  labs(x = "Type of cuisine (hpg_genre_name)", y = "Number of hpg restaurants")
  
p2 <- hpg_store %>%
  mutate(area = str_sub(hpg_area_name, 1, 20)) %>%
  group_by(area) %>%
  count() %>%
  ungroup() %>%
  top_n(15,n) %>%
  ggplot(aes(reorder(area, n, FUN = min) ,n, fill = area)) +
  geom_col() +
  theme(legend.position = "none") +
  coord_flip() +
  labs(x = "Top 15 areas (hpg_area_name)", y = "Number of hpg restaurants")

layout <- matrix(c(1,2),1,2,byrow=TRUE)
multiplot(p1, p2, layout=layout)

Here we have truncated the hpg_area_name to 20 characters to make the plot more readable.

We find:

• The hpg description contains a larger variety of genres than in the air data. Here, Japanese style appears to contain many more places that are categorised more specifically in the air data. The same applies to International cuisine.

• In the top 15 area we find again Tokyo and Osaka to be prominently present.

# Create a map centered at a specific location
m = folium.Map(location=[hpg_store['latitude'].median(), 
                         hpg_store['longitude'].median()],
                         zoom_start=7, 
                         width=1500, height=800)

# Add tiles (you can choose different providers)
folium.TileLayer(tiles='CartoDB positron').add_to(m)

## <folium.raster_layers.TileLayer object at 0x7f7ef3726410>

# Create a MarkerCluster object
marker_cluster = MarkerCluster().add_to(m)

## Also working
# hpg_store.apply(lambda row:folium.Marker(
#                   location=[row['latitude'], row['longitude']],                        
#                   popup=row['hpg_store_id'],icon=None,
#                   tooltip=row['hpg_genre_name']).add_to(marker_cluster), 
#                   axis=1)

# Define a function to add markers
def add_marker(row):
    folium.Marker(location=[row['latitude'], row['longitude']],
                  popup=row['hpg_store_id'],
                  icon=None,
                  tooltip=row['hpg_genre_name']).add_to(marker_cluster)

# Apply the function to each row of the DataFrame
hpg_store.apply(add_marker, axis=1)

## 0       None
## 1       None
## 2       None
## 3       None
## 4       None
##         ... 
## 4685    None
## 4686    None
## 4687    None
## 4688    None
## 4689    None
## Length: 4690, dtype: object

# Display the map
m

Make this Notebook Trusted to load map: File -> Trust Notebook

p1_data = hpg_store['hpg_genre_name'].value_counts().reset_index()
p1_data.columns = ['hpg_genre_name', 'count']
p1_data = p1_data.sort_values(by=['count'], ascending=False).reset_index(drop=True)

p2_data = hpg_store['hpg_area_name'].value_counts().nlargest(15).reset_index()
p2_data.columns = ['hpg_area_name', 'count']
p2_data = p2_data.sort_values(['count'], ascending=False).reset_index(drop=True)


# Multiplot layout
fig = plt.figure(figsize=(12, 8))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

ax1 = fig.add_subplot(gs[:, 0])
ax2 = fig.add_subplot(gs[:, 1])

# Plot 1
p1= sns.barplot(data=p1_data, x='count', y='hpg_genre_name', order=p1_data['hpg_genre_name'],
                palette='dark', ax=ax1, legend=False)
p1= ax1.set_xlabel('Number of hpg restaurants')
p1= ax1.set_ylabel("Type of cuisine")
#p1= ax1.set_title("Number of hpg restaurants by cuisine type")
#p1= ax1.set_xticklabels(ax1.get_xticklabels(), rotation=0)
#p1= ax1.yaxis.set_major_locator(mdates.AutoDateLocator())
#p1= plt.legend("")

# Plot 2
p2= sns.barplot(data=p2_data, x='count', y='hpg_area_name', order=p2_data['hpg_area_name'],
                palette='bright', ax=ax2, legend=False, width=0.8)
p2= ax2.set_xlabel("Number of hpg restaurants")
p2= ax2.set_ylabel("Top 15 areas")
#p2= ax2.set_title("Top 10 areas with most hpg restaurants")
#p2= ax2.set_xticklabels(ax2.get_xticklabels(), rotation=0)
#p2= ax2.yaxis.set_major_locator(mdates.AutoDateLocator())
p2= plt.legend("")
plt.tight_layout()
plt.show()

4.6 Holidays

Let’s have a quick look at the holidays. We’ll plot how many there are in total and also how they are distributed during our prediction time range in 2017 and the corresponding time in 2016:

foo <- holidays %>%
  mutate(wday = wday(date, week_start = 1))

p1 <- foo %>%
  ggplot(aes(holiday_flg, fill = holiday_flg)) +
  geom_bar() +
  theme(legend.position = "none")
  
p2 <- foo %>%
  filter(date > ymd("2016-04-15") & date < ymd("2016-06-01")) %>%
  ggplot(aes(date, holiday_flg, color = holiday_flg)) +
  geom_point(size = 2) +
  theme(legend.position = "none") +
  labs(x = "2016 date")

p3 <- foo %>%
  filter(date > ymd("2017-04-15") & date < ymd("2017-06-01")) %>%
  ggplot(aes(date, holiday_flg, color = holiday_flg)) +
  geom_point(size = 2) +
  theme(legend.position = "none") +
  labs(x = "2017 date")

layout <- matrix(c(1,1,2,3),2,2,byrow=FALSE)
multiplot(p1, p2, p3, layout=layout)

We find:

• The same days were holidays in late Apr / May in 2016 as in 2017.

• There are about 7% holidays in our data:

holidays %>% summarise(frac = mean(holiday_flg))

##         frac
## 1 0.06769826

# Convert 'date' column to datetime if it's not already
holidays['date'] = pd.to_datetime(holidays['date'])

# Plot 1
p1_data = holidays['holiday_flg'].value_counts().reset_index()
p1_data.columns = ['holiday_flg', 'count']
p2_data = holidays[(holidays['date'] > '2016-04-15') & (holidays['date'] < '2016-06-01')]
p2_data['holiday_flg'] = p2_data['holiday_flg'].astype('category')
p3_data = holidays[(holidays['date'] > '2017-04-15') & (holidays['date'] < '2017-06-01')]


# Multiplot layout
fig = plt.figure(figsize=(6, 4))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')
locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

ax1 = fig.add_subplot(gs[:, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[1, 1])


# Plot1
p1= sns.barplot(data=p1_data, x='holiday_flg', y='count', palette='viridis',  
            ax=ax1, legend=False)
p1= ax1.set_xlabel('Holiday Flag')
#p1= ax1.set_title("Distribution of Holiday Flag")
p1= plt.legend("")

# Plot 2
p2= sns.scatterplot(data=p2_data, x='date', y='holiday_flg', hue='holiday_flg', 
                     palette='viridis', ax=ax2, legend=False)
p2.set_yticks([1.0, 0.0], ["True","False"])
p2= ax2.set_xlabel('2016')
p2= ax2.set_title("2016")
#p2 = ax2.set(xticklabels = p2_data['date'].dt.strftime('%d %b'))
p2= fig.autofmt_xdate() 
p2= ax2.set_ylabel('')
p2= plt.legend("")
p2= ax2.xaxis.set_major_locator(mdates.AutoDateLocator())

# Plot 3
p3= sns.scatterplot(data=p3_data, x='date', y='holiday_flg', hue='holiday_flg', palette='viridis', ax=ax3, legend=False)
p3.set_yticks([1.0, 0.0], ["True","False"])
p3 = ax3.set(xticklabels = p3_data['date'].dt.strftime('%d %b'))
p3= fig.autofmt_xdate()
p3= ax3.set_ylabel('')
p3= ax3.xaxis.set_major_locator(mdates.AutoDateLocator())
p3= plt.xlabel("2017")
#p3= plt.title("Holiday Flag in 2017")
p3= plt.legend("")


plt.tight_layout( pad=0.4, w_pad=0.5, h_pad=1)
plt.show()

frac = holidays['holiday_flg'].mean()
print(frac.round(3))

## 0.068

4.7 Test data set

The following plot visualises the time range of the train vs test data sets:

foo <- air_visits %>%
  rename(date = visit_date) %>%
  distinct(date) %>%
  mutate(dset = "train")

bar <- test %>%
  separate(id, c("foo", "bar", "date"), sep = "_") %>%
  mutate(date = ymd(date)) %>%
  distinct(date) %>%
  mutate(dset = "test")

foo <- foo %>%
  bind_rows(bar) %>%
  mutate(year = year(date))
year(foo$date) <- 2017

foo %>%
  filter(!is.na(date)) %>%
  mutate(year = fct_relevel(as.factor(year), c("2017","2016"))) %>%
  ggplot(aes(date, year, color = dset)) +
  geom_point(shape = "|", size = 10) +
  scale_x_date(date_labels = "%B", date_breaks = "1 month") +
  #scale_y_reverse() +
  theme(legend.position = "bottom", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9)) +
  labs(color = "Data set") +
  guides(color = guide_legend(override.aes = list(size = 4, pch = 15)))

# Renaming and selecting distinct dates for 'foo'
foo = air_visits.rename(columns={'visit_date': 'date'}).drop_duplicates(subset=['date'])
foo['dset'] = 'train'

# Processing 'bar'
test['date'] = pd.to_datetime(test['id'].str.split('_').str[-1])
bar = test[['date']].drop_duplicates()
bar['dset'] = 'test'

# Combining 'foo' and 'bar'
foo = pd.concat([foo, bar], ignore_index=True)

# Setting 'year' column
foo['year'] = foo['date'].dt.strftime('%Y').astype('category')

# Filtering out NA dates
foo = foo.dropna(subset=['date'])

# Adding a 'Months' column
foo['Months'] = foo['date'].dt.strftime('%B')

# Set up the plot
plt.figure(figsize=(8, 4))
#p= sns.set(rc={'figure.figsize':(4,2)})
plt.style.use('ggplot')

# Create a scatter plot using Seaborn
p= sns.scatterplot(data=foo, x='Months', y= 'year' , hue='dset', color= 'dset',
                   #palette={'train': 'blue', 'test': 'red'}, 
                   marker='*',
                   s=250)
# Format the tick labels to display the month name
#p.invert_yaxis()
p= plt.xticks(rotation=35)
p= plt.tick_params(axis='x', pad=-5, labelsize=8)
plt.margins(y=1)
plt.legend(bbox_to_anchor=(0.99, 0.01), loc='lower right', borderaxespad=0)
plt.show(p)

5 Feature relations

After looking at every data set individually, let’s get to the real fun and start combining them. This will tell us something about the relations between the various features and how these relationsy might affect the visitor numbers. Any signal we find will need to be interpreted in the context of the individual feature distributions; which is why it was one of our first steps to study those.

5.1 Visitors per genre

Our first plot of the multi-feature space deals with the average number of air restaurant visitors broken down by type of cuisine; i.e. the air_genre_name. We use a facet plot to distinguish the time series for the 14 categories. Note the logarithmic y-axis:

foo <- air_visits %>%
  left_join(air_store, by = "air_store_id")

foo %>%
  group_by(visit_date, air_genre_name) %>%
  summarise(mean_visitors = mean(visitors)) %>%
  ungroup() %>%
  ggplot(aes(visit_date, mean_visitors, color = air_genre_name)) +
  geom_line() +
  labs(y = "Average number of visitors to 'air' restaurants", x = "Date") +
  theme(legend.position = "none") +
  scale_y_log10() +
  facet_wrap(~ air_genre_name)

## `summarise()` has grouped output by 'visit_date'. You can override using the
## `.groups` argument.

We find:

• The mean values range between 10 and 100 visitors per genre per day. Within each category, the long-term trend looks reasonably stable. There is an upward trend for Creative Cuisine and Okonomiyaki et al., while the popularity of Asian food has been declining since late 2016.

• The low-count time series like Karaoke or Asian (see Fig. 6) are understandably more noisy than the genres with higher numbers of visitors. Still, Asian restaurants appear to be very popular despite (or because of?) their rarity.

In all of the curves we see the familiar weekly variation, so let’s look in more detail at the mean visitor numbers per week day and genre. We also add to this a series of ridgeline plots via the ggridges package. Ridgeline plots allow for a quick comparison of semi-overlapping (density) curves. Here we show the distribution of visitors per day for each genre. Through a little bit of ggplot magic, the y-axis labels in between those two plots refer to both of them:

p1 <- foo %>%
  mutate(wday = wday(visit_date, label = TRUE, week_start = 1)) %>%
  group_by(wday, air_genre_name) %>%
  summarise(mean_visitors = mean(visitors)) %>%
  ggplot(aes(air_genre_name, mean_visitors, color = wday)) +
  geom_point(size = 4) +
  theme(legend.position = "left", axis.text.y = element_blank(),
        plot.title = element_text(size = 14)) +
  coord_flip() +
  labs(x = "") +
  scale_x_discrete(position = "top") +
  ggtitle("air_genre_name") +
  scale_color_hue()

## `summarise()` has grouped output by 'wday'. You can override using the
## `.groups` argument.

p2 <- foo %>%
  ggplot(aes(visitors, air_genre_name, fill = air_genre_name)) +
  geom_density_ridges(bandwidth = 0.1) +
  scale_x_log10() +
  theme(legend.position = "none") +
  labs(y = "") +
  scale_fill_cyclical(values = c("blue", "red"))

layout <- matrix(c(1,1,2,2,2),1,5,byrow=TRUE)
multiplot(p1, p2, layout=layout)

Here each colour corresponds to a day of the week. Red-ish coulours are the weekend, while the cooler colours are the middle of the week. Monday is a dark orange.

We find:

• The biggest difference between weekend and weekdays exists for the Karaoke bars, which rule the weekend. A similar trend, although with a considerably smaller gap, can be seen for the International cuisine.

• No genre really goes against the trend of busier weekends. The smallest variations are in the generic Other category, the Japanese food, and also the Korean cuisine which is the only category where Fridays are the busiest days. General Bars/Cocktail are notably unpopular overall.

• The density curves confirm the impression we got from the week-day distribution: the Asian restaurants have rarely less than 10 visitors per date and the Karaoke places show a very broad distribution due to the strong impact of the weekends. Note the logarithmic x-axis

# Merge 'air_visits' and 'air_store' on the column 'air_store_id'
foo = pd.merge(air_visits, air_store, on='air_store_id', how='left')

#Grouping and summarizing data
summary_data = foo.groupby(['visit_date', 'air_genre_name'],
                           observed=True)['visitors'].mean().reset_index()

fig = plt.figure(figsize = (4,2))
plt.style.use('ggplot')

# Set up the FacetGrid
g = sns.FacetGrid(summary_data, col="air_genre_name",
                  col_wrap=4, height=2, aspect= 1,
                  sharex=True)

# Create line plots for each genre
p = g.map_dataframe(sns.lineplot, x='visit_date', 
                y='visitors', hue='air_genre_name')
                
# Resize facet titles
p= g.set_titles(col_template="{col_name}", 
               size = 8, backgroundcolor='#DDDDDD', pad=2
           # bbox={'facecolor': '#DDDDDD', 'alpha': 0, 'pad': 0}
            )
p= g.tick_params(axis='x', pad=0, labelsize= 6)
p= g.set_xlabels(fontsize=6, label="Date")
p= g.set_ylabels(fontsize=8 )#,label="Average number of visitors")
# Set labels and title
#g.set_axis_labels(x_var="Date",y_var= "Average number of visitors")
#g.add_legend(title="gendre")

for ax in g.axes.flat:
    for label in ax.get_xticklabels():
        label.set_rotation(45)

# Apply logarithmic scale to y-axis
p= g.set(yscale="log")
# Adjust the layout
p= g.tight_layout()

# Show the plot
plt.show(p)

# Extracting weekday
foo['wday'] = foo['visit_date'].dt.day_name()

# Data Processing for p1
p1_data = foo.groupby(['wday', 'air_genre_name'], observed=True).agg(mean_visitors=('visitors', 'mean')).reset_index()

# Data Processing for p2 (Assuming 'foo' DataFrame is available)
p2_data = foo.copy()
# Apply necessary transformations to 'p2_data' DataFrame

# Create a 2x2 grid
fig = plt.figure(figsize=(12, 8))
gs = GridSpec(2, 2, figure=fig)

# Plot 1 (Top Left)
ax1 = fig.add_subplot(gs[:, 0])
sns.scatterplot(data=p1_data,
                y='air_genre_name',
                x='mean_visitors',
                hue='wday',
                size=4,
                #palette='viridis', 
                ax=ax1)
# Set the figure size using rcParams
ax1.set_title('air_genre_name', fontsize=8)
ax1.set_xlabel('')
ax1.set_ylabel('')
ax1.legend(title='wday', loc='center right')
#ax1.legend("")



ax2 = fig.add_subplot(gs[:, 1],sharex=True)

## 'other' must be an instance of matplotlib.axes._base._AxesBase, not a bool

## Plot 2 (Top Right)
ax2 = fig.add_subplot(gs[:, 1])
for genre in p2_data['air_genre_name'].unique():
    sns.kdeplot(data=p2_data, #p2_data[p2_data['air_genre_name'] == genre]
                x='visitors',
                hue='air_genre_name',
                fill=True,
                common_norm=False,
                levels=30,
                label=genre,
                ax=ax2)
ax2.set_xlabel('')
ax2.set_ylabel('')
ax2.set_title('')
#ax2.legend("",loc=2)
p= ax2.set_xlim(-50, 200)


# Adjust layout
p= plt.tight_layout()

# Show the plots
plt.show(p)

# Data Processing for p2 (Assuming 'foo' DataFrame is available)
p2_data = foo.copy()

fig = plt.figure(figsize=(10, 8))

# Plot 2 (Bottom)
pal = sns.cubehelix_palette(10, rot=-.25, light=.7)
g = sns.FacetGrid(p2_data, 
                 row="air_genre_name", 
                 hue="air_genre_name", #palette=pal,
                 aspect=15, height=.5
                 )
p= g.map(sns.kdeplot, 'visitors',
      bw_adjust=.5, clip_on=False,
      fill=True, alpha=1, linewidth=.5)
      
p= g.map(sns.kdeplot, 'visitors', clip_on=False, color="black", lw=2, bw_adjust=.5)

# Define and use a simple function to label the plot in axes coordinates
def label(x, color, label):
    ax = plt.gca()
    ax.text(0, .2, label,  color=color, #fontweight="bold",
            ha="right", va="center", transform=ax.transAxes)

p= g.map(label, "visitors")

p= g.set(xlim=(-50, 1000))
p= g.set_titles("")
p= g.set(yticks=[], ylabel="")
p= g.despine(bottom=True, left=True)
p= g.fig.subplots_adjust(hspace=-.25)

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show(p)

5.2 The impact of holidays

We will study the influence of holidays on our visitor numbers by comparing the statistics for days with holidays vs those without holiday flag:

foo <- air_visits %>%
  mutate(calendar_date = as.character(visit_date)) %>%
  left_join(holidays, by = "calendar_date")

p1 <- foo %>%
  ggplot(aes(holiday_flg, visitors, color = holiday_flg)) +
  geom_boxplot() +
  scale_y_log10() +
  theme(legend.position = "none")

p2 <- foo %>%
  mutate(wday = wday(date, label = TRUE, week_start = 1)) %>%
  group_by(wday, holiday_flg) %>%
  summarise(mean_visitors = mean(visitors)) %>%
  ggplot(aes(wday, mean_visitors, color = holiday_flg)) +
  geom_point(size = 4) +
  theme(legend.position = "none") +
  labs(y = "Average number of visitors")

## `summarise()` has grouped output by 'wday'. You can override using the
## `.groups` argument.

layout <- matrix(c(1,2),1,2,byrow=TRUE)
multiplot(p1, p2, layout=layout)

We find:

• Overall, holidays don’t have any impact on the average visitor numbers (left panel). As so often, more information is hidden in the details.

• While a weekend holiday has little impact on the visitor numbers, and even decreases them slightly, there is a much more pronounced effect for the weekdays; especially Monday and Tuesday (right panel).

from matplotlib import pyplot as plt, dates

# Data Processing
foo = air_visits.copy()
#foo['calendar_date'] = foo['visit_date'].dt.strftime('%Y-%m-%d')
foo['calendar_date'] = foo['visit_date'].astype(str)
#foo = foo.merge(holidays, left_on='calendar_date', right_on='date', how='left')
foo = pd.merge(foo, holidays, left_on='calendar_date', how='left', right_on = 'calendar_date')


# Data Processing for p1
p1_data = foo.copy()
p1_data['holiday_flg'] = p1_data['holiday_flg'].astype(bool)  # Convert to boolean
p1_data['wday'] = p1_data['visit_date'].dt.day_name()  # Extract weekday

# Data Processing for p2

# Data Processing for Plot 2
p2_data = foo.copy()
order = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
p2_data['wday'] = pd.Categorical(p2_data['visit_date'].dt.day_name(), categories= order, ordered=True)
p2_data['wdayn'] = p2_data['date'].dt.dayofweek  # Extract weekday as a number (0-6)  
p2_data = p2_data.groupby(['wday', 'holiday_flg', 'wdayn'], observed=True).agg(mean_visitors=('visitors', 'mean')).reset_index()
p2_data['wdayn'] = pd.Categorical(p2_data['wdayn'], categories=[0,1,2,3,4,5,6], ordered=True)  # Sort weekdays
#p2_data['wdayn'] = p2_data['wdayn'].dt.day_name()

# Create a 1x2 grid
fig, axes = plt.subplots(1, 2, figsize=(10, 4))
locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

plt.style.use('ggplot')

# Plot 1 (p1)
flierprops = dict(marker='o', markerfacecolor='r', markersize=10,
                  linestyle='none', markeredgecolor='b')
sns.boxplot(data=p1_data, x='holiday_flg', y='visitors',
              hue='holiday_flg', 
              #flierprops=flierprops,
              fill=False,
              #dodge=False, 
              showfliers = True,
              ax=axes[0])
axes[0].set_yscale('log')
#axes[0].set_title('Boxplot of Visitors on Holidays')
#axes[0].set_xlabel('Holiday')
axes[0].set_ylabel('Visitors (log scale)')
axes[0].legend('')

# Plot 2 (p2)
sns.scatterplot(data=p2_data, x='wday', y='mean_visitors', 
                hue='holiday_flg', 
                ax=axes[1], s=50)
#axes[1].set_title('Average Visitors by Weekday')
axes[1].set_xlabel('wday')
axes[1].set_ylabel('Average Visitors')
axes[1].xaxis.set_ticks(order)
axes[1].set_xticklabels(axes[1].get_xticklabels(), rotation=45)
#axes[1].xaxis.set_major_formatter(dates.DateFormatter('%a'))
axes[1].legend('')


# Adjust layout
plt.tight_layout()

# Show the plots
plt.show()

5.3 Restaurants per area and the effect on visitor numbers

Our next exploration follows from a simple thought: if gastropubs are popular and we own the only gastropub in the area then we can expect lots of customers. If there are twelve other gastropubs in our street then, try as we might, some of those customers will venture into other establishments. Economists tell us that we can ultimately expect a convergence towards an equilibrium between supply and demand. But for snapshots like our data set, and for relatively localised areas, there might still be merit in investigating restaurant clustering. Therefore, let’s study the number of restaurants of a certain genre per area and their impact on visitor numbers.

We begin with an overview plot of the frequency of certain genres per area for the two data sets of air and hpg stores. This could have well been a part of the previous chapter, but I only just thought about it ;-) . The following count plots show which genres exist in which areas (names truncated). The size of the dots is proportional to the number of cases:

air_store %>%
  mutate(area = str_sub(air_area_name, 1, 12)) %>%
  ggplot(aes(area, air_genre_name)) +
  geom_count(colour = "blue") +
  theme(legend.position = "bottom", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9))

We find:

• Some areas have lots of restaurants and much variety, whereas others contain only a single air restaurant. Large parts of the parameter space are empty.

• Similarly, some cuisines like Izakaya or Cafe are pretty ubiqutous, whereas others can only be found in a few areas. Note, that the only 2 Karaoke bars in the air sample are in Hokkaido Sapporo-shi Minami 3 Jonishi, whereas the only 2 International cuisine restaurants as well as the only two Asian places can be found in Tokyo-to Shibuya-ku Shibuya.

The same kind of plot for the hpg data looks similar albeit more busy due to the larger number of genres:

hpg_store %>%
  mutate(area = str_sub(hpg_area_name, 1, 10)) %>%
  ggplot(aes(area, hpg_genre_name)) +
  geom_count(colour = "red") +
  theme(legend.position = "bottom", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9))

We find:

• Also here there are busy areas and those with only a few restaurants. Unsurprisingly, Tokyo features prominently in the areas with a lot of culinary diversity.

• Japanese style and International cuisine are popular pretty much everywhere. Amusement bars and Udon/Soba places are rare, as are Shanghai food or Dim Sum.

The count plots tell us that there is a distribution of how many restaurants of a certain genre can be found per area. Here we look at these distributions in detail via boxplots with overlayed jitter plots. The genres are ordered by decreasing mean cases per area, i.e. the mean of a horizontal sequence of dots in a count plot. The we overlay the indvidual data point and assign each dot a random jitter to visually separate otherwise overlapping data. Here, the y axis (i.e. Occurences per area) correspond to the size of the dots in the count plots above. We’re using single plots here, instead of panels, because these plots are quite detailed. Note the logarithmic y-axes.

We start with the air data:

air_store %>%
  group_by(air_genre_name, air_area_name) %>%
  count() %>%
  ggplot(aes(reorder(air_genre_name, n, FUN = mean), n)) +
  geom_boxplot() +
  geom_jitter(color = "blue") +
  scale_y_log10() +
  coord_flip() +
  labs(x = "Air genre", y = "Occurences per air area")

We find:

• Only few genres have medians of more than 2 restaurants per area. Examples are Italian/French restaurants or Bar/Cocktail places, which are more likely to be found in groups of more than 2 per area.

• For the majority of genres the distribution is firmly clustered around 2 cases per area with a bit of scatter towards higher numbers. Cafes have the highest number with 26 occurences in a single area (Fukuoka-ken Fukuoka-shi Daimyō).

• Curiously, the minimum here is 2, not 1. This means that there is no air restaurant that is the only one of it’s genre in any area. You can see that also on the map in Fig. 5: whenever there is a group of 2 restaurants at the same area coordinates they have the same genre (but different air_store_ids). Similarly, there are no single occurrences of a genre in any larger group per area. (There exist odd numbers of occurences though, i.e. 3 or 5 of the same genre per area.) I’m not quite sure what to make of that, since it seems too perfectly matched to be true. Could it have something to do with the way the air data have been selected? Might it be a bug in assigning genre names? I checked a few examples of 2 restaurants in one spot and they have different visitor numbers on the same day, e.g. for this pair of Dining Bars, indicating that we don’t simply have a problem of single entries being duplicated here:

air_store %>%
  filter(air_store_id == "air_b5598d12d1b84890" | air_store_id == "air_bbe1c1a47e09f161")

##            air_store_id air_genre_name                 air_area_name latitude
## 1: air_bbe1c1a47e09f161     Dining bar Tōkyō-to Setagaya-ku Kitazawa 35.66266
## 2: air_b5598d12d1b84890     Dining bar Tōkyō-to Setagaya-ku Kitazawa 35.66266
##    longitude
## 1:  139.6683
## 2:  139.6683

air_visits %>%
  filter(air_store_id == "air_b5598d12d1b84890" | air_store_id == "air_bbe1c1a47e09f161") %>%
  arrange(visit_date) %>%
  head(10)

##             air_store_id visit_date visitors
##  1: air_bbe1c1a47e09f161 2016-07-01        7
##  2: air_b5598d12d1b84890 2016-07-01        5
##  3: air_b5598d12d1b84890 2016-07-02       14
##  4: air_b5598d12d1b84890 2016-07-03        6
##  5: air_b5598d12d1b84890 2016-07-04        6
##  6: air_b5598d12d1b84890 2016-07-05        5
##  7: air_b5598d12d1b84890 2016-07-06        5
##  8: air_bbe1c1a47e09f161 2016-07-07        1
##  9: air_bbe1c1a47e09f161 2016-07-08        7
## 10: air_b5598d12d1b84890 2016-07-08       10

Now we look at the same distribution for the HPG restaurants:

foobar <- hpg_store %>%
  group_by(hpg_genre_name, hpg_area_name) %>%
  count()

foobar %>%
  ggplot(aes(reorder(hpg_genre_name, n, FUN = mean), n)) +
  geom_boxplot() +
  geom_jitter(color = "red") +
  scale_y_log10() +
  coord_flip() +
  labs(x = "hpg genre", y = "Cases per hpg area")

We find:

• Here we clearly have a minimum of 1 genre per area, and also much more variety in median cases due to the higher overall numbers.

• The most extreme genre is Japanese style for which the median is just above 10 restaurants per area. Alongside of this, there a number of other genres for which the lower box hinge is not touching the minimum of 1 case per area.

Using the information on the number of genres in each area we can now proceed to quantify the clustering, or crowdedness, of our data set and relate it to the visitor numbers. The next plot first shows the overall distribution of the air and hpg data points from the last two plots (i.e. cases of the same genre per area).

In addition, we estimate the mean visitor numbers for each clustering case. For this, we first take the mean of the log1p-transformed visitor numbers (per genre and area) and then compute the mean and standard deviation of these numbers for each case, i.e. number of occurences of the same genre in an area. (log1p means log(x+1) and is intended to make the visitors number distribution more normal; see Fig. 1).

foo <- air_visits %>%
  left_join(air_store, by = "air_store_id")

bar <- air_store %>%
  group_by(air_genre_name, air_area_name) %>%
  count()

foobar <- hpg_store %>%
  group_by(hpg_genre_name, hpg_area_name) %>%
  count()

p1 <- bar %>%
  ggplot(aes(n)) +
  geom_histogram(fill = "blue", binwidth = 1) +
  labs(x = "Air genres per area")

p2 <- foobar %>%
  ggplot(aes(n)) +
  geom_histogram(fill = "red", binwidth = 1) +
  labs(x = "HPG genres per area")

p3 <- foo %>%
  group_by(air_genre_name, air_area_name) %>%
  summarise(mean_log_visit = mean(log1p(visitors))) %>%
  left_join(bar, by = c("air_genre_name","air_area_name")) %>%
  group_by(n) %>%
  summarise(mean_mlv = mean(mean_log_visit),
            sd_mlv = sd(mean_log_visit)) %>%
  replace_na(list(sd_mlv = 0)) %>%
  ggplot(aes(n, mean_mlv)) +
  geom_point(color = "blue", size = 4) +
  geom_errorbar(aes(ymin = mean_mlv - sd_mlv, ymax = mean_mlv + sd_mlv), width = 0.5, size = 0.7, color = "blue") +
  labs(x = "Cases of identical Air genres per area", y = "Mean +/- SD of\n mean log1p visitors")

## `summarise()` has grouped output by 'air_genre_name'. You can override using
## the `.groups` argument.

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

layout <- matrix(c(1,2,3,3),2,2,byrow=TRUE)
multiplot(p1, p2, p3, layout=layout)

We find:

• Upper panels: The numbers of cases of identical genres in the same area drops quickly, possibly exponentially, from the maxima of 2 and 1 for air and hpg data sets, respectively. There is a longer tail towards larger case numbers, with a possible 2nd peak around 8 for air and about 13 for hpg.

• Lower panel: The log1p means of visitor numbers show relatively large spread and are perfectly consistent in the range from 2 cases to 9. From 10 cases upward we simply don’t have the numbers to measure a spread: there are two data points with 11 cases per area and otherwise it’s just a single measurement. However, it is noteworthy that the scatter among all the data points > 9 cases is pretty low, and that the lie notably higher than the means of the points <= 9. Now, that could simply mean that those high visitor numbers are not being brought down by small (less busy?) areas, but that in itself is an interesting result.

• Note that the scatter plot in the lower panel mixes treats all the clustering/crowding cases regardless of genre. We can of course only draw this plot for the air data for which we have visitor numbers.

# Create a new column 'area' by extracting the first 12 characters from 'air_area_name'
air_store['area'] = air_store['air_area_name'].str[:12]
#Count the frequency of each combination of 'area' and 'air_genre_name'
counts = air_store.groupby(['area', 'air_genre_name'], observed=True).size().reset_index(name='count')
# Plotting
plt.figure(figsize=(8, 4))
sns.scatterplot(data=counts, x='area', y='air_genre_name',
                 size='count', color='blue', legend=True)
# Rotate x-axis labels for better visibility
plt.xticks(rotation=45, ha='right')

## ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [Text(0, 0, 'Fukuoka-ken '), Text(1, 0, 'Hiroshima-ke'), Text(2, 0, 'Hokkaidō Aba'), Text(3, 0, 'Hokkaidō Asa'), Text(4, 0, 'Hokkaidō Kat'), Text(5, 0, 'Hokkaidō Sap'), Text(6, 0, 'Hyōgo-ken Am'), Text(7, 0, 'Hyōgo-ken Hi'), Text(8, 0, 'Hyōgo-ken Ka'), Text(9, 0, 'Hyōgo-ken Kō'), Text(10, 0, 'Hyōgo-ken Ni'), Text(11, 0, 'Hyōgo-ken Ta'), Text(12, 0, 'Miyagi-ken S'), Text(13, 0, 'Niigata-ken '), Text(14, 0, 'Shizuoka-ken'), Text(15, 0, 'Tōkyō-to Ada'), Text(16, 0, 'Tōkyō-to Bun'), Text(17, 0, 'Tōkyō-to Chi'), Text(18, 0, 'Tōkyō-to Chū'), Text(19, 0, 'Tōkyō-to Edo'), Text(20, 0, 'Tōkyō-to Fuc'), Text(21, 0, 'Tōkyō-to Ita'), Text(22, 0, 'Tōkyō-to Kat'), Text(23, 0, 'Tōkyō-to Kit'), Text(24, 0, 'Tōkyō-to Kog'), Text(25, 0, 'Tōkyō-to Kōt'), Text(26, 0, 'Tōkyō-to Mac'), Text(27, 0, 'Tōkyō-to Meg'), Text(28, 0, 'Tōkyō-to Min'), Text(29, 0, 'Tōkyō-to Mus'), Text(30, 0, 'Tōkyō-to Nak'), Text(31, 0, 'Tōkyō-to Ner'), Text(32, 0, 'Tōkyō-to Set'), Text(33, 0, 'Tōkyō-to Shi'), Text(34, 0, 'Tōkyō-to Sug'), Text(35, 0, 'Tōkyō-to Tac'), Text(36, 0, 'Tōkyō-to Tai'), Text(37, 0, 'Tōkyō-to Tos'), Text(38, 0, 'Tōkyō-to Ōta'), Text(39, 0, 'Ōsaka-fu Hig'), Text(40, 0, 'Ōsaka-fu Ney'), Text(41, 0, 'Ōsaka-fu Sak'), Text(42, 0, 'Ōsaka-fu Sui'), Text(43, 0, 'Ōsaka-fu Ōsa')])

# Set labels and title
plt.xlabel('Area')
plt.ylabel('Air Genre Name')
plt.tick_params(axis='x', pad=0, labelsize=7)
# Adjust legend position
plt.legend(bbox_to_anchor = (1,1),loc='upper left')

# Show the plot
plt.show()

# Create a new column 'area' by extracting the first 12 characters from 'air_area_name'
hpg_store['area'] = hpg_store['hpg_area_name'].str[:10]
#Count the frequency of each combination of 'area' and 'air_genre_name'
counts = hpg_store.groupby(['area', 'hpg_genre_name'], observed=True).size().reset_index(name='count')
# Plotting
plt.figure(figsize=(8, 4))
sns.scatterplot(data=counts, x='area', y='hpg_genre_name',
                 size='count', color='red', legend=True)
# Rotate x-axis labels for better visibility
plt.xticks(rotation=45, ha='right')

## ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [Text(0, 0, 'Fukuoka-ke'), Text(1, 0, 'Hiroshima-'), Text(2, 0, 'Hokkaidō A'), Text(3, 0, 'Hokkaidō H'), Text(4, 0, 'Hokkaidō S'), Text(5, 0, 'Hokkaidō T'), Text(6, 0, 'Hyōgo-ken '), Text(7, 0, 'Kanagawa-k'), Text(8, 0, 'Miyagi-ken'), Text(9, 0, 'Niigata-ke'), Text(10, 0, 'None None '), Text(11, 0, 'Osaka Pref'), Text(12, 0, 'Saitama-ke'), Text(13, 0, 'Shizuoka-k'), Text(14, 0, 'Tōkyō-to A'), Text(15, 0, 'Tōkyō-to B'), Text(16, 0, 'Tōkyō-to C'), Text(17, 0, 'Tōkyō-to F'), Text(18, 0, 'Tōkyō-to H'), Text(19, 0, 'Tōkyō-to I'), Text(20, 0, 'Tōkyō-to K'), Text(21, 0, 'Tōkyō-to M'), Text(22, 0, 'Tōkyō-to N'), Text(23, 0, 'Tōkyō-to S'), Text(24, 0, 'Tōkyō-to T'), Text(25, 0, 'Ōsaka-fu H'), Text(26, 0, 'Ōsaka-fu I'), Text(27, 0, 'Ōsaka-fu K'), Text(28, 0, 'Ōsaka-fu M'), Text(29, 0, 'Ōsaka-fu N'), Text(30, 0, 'Ōsaka-fu S'), Text(31, 0, 'Ōsaka-fu T'), Text(32, 0, 'Ōsaka-fu Ō')])

# Set labels and title
plt.xlabel('Area')
plt.ylabel('HPG Genre Name')
plt.tick_params(axis='x', pad=0, labelsize=7)
plt.tick_params(axis='y', pad=0, labelsize=7)
# Adjust legend position
plt.legend(bbox_to_anchor = (1,1),loc='upper left')

# Show the plot
plt.show()

# Group by 'air_genre_name' and 'air_area_name', and count the frequency
counts = air_store.groupby(['air_genre_name', 'air_area_name'], observed=True).size().reset_index(name='count')

# Reorder 'air_genre_name' by count
order = counts.groupby('air_genre_name', observed=True)['count'].mean().sort_values().index

# Plotting
plt.figure(figsize=(8, 6))
sns.boxplot(data=counts, y='air_genre_name', x='count', order=order, hue='air_genre_name' ,palette='viridis')
sns.stripplot(data=counts, y='air_genre_name', x='count', order=order, color='blue', size=3)

# Set labels and title
plt.xlabel('Occurences per air area')
plt.ylabel('Air genre')
plt.xscale('log')

# Show the plot
plt.show()

 air_store[air_store['air_store_id'].isin(["air_b5598d12d1b84890", "air_bbe1c1a47e09f161"])]

## unexpected indent (<string>, line 1)

selected_visits = air_visits[air_visits['air_store_id'].isin(["air_b5598d12d1b84890", "air_bbe1c1a47e09f161"])]
selected_visits.sort_values(by='visit_date').head(10)

##                 air_store_id visit_date  visitors
## 239978  air_bbe1c1a47e09f161 2016-07-01         7
## 250021  air_b5598d12d1b84890 2016-07-01         5
## 250022  air_b5598d12d1b84890 2016-07-02        14
## 250023  air_b5598d12d1b84890 2016-07-03         6
## 250024  air_b5598d12d1b84890 2016-07-04         6
## 250025  air_b5598d12d1b84890 2016-07-05         5
## 250026  air_b5598d12d1b84890 2016-07-06         5
## 239979  air_bbe1c1a47e09f161 2016-07-07         1
## 250027  air_b5598d12d1b84890 2016-07-08        10
## 239980  air_bbe1c1a47e09f161 2016-07-08         7

foobar = hpg_store.groupby(['hpg_genre_name', 'hpg_area_name'], observed=True).size().reset_index(name='n')

# Reorder 'hpg_genre_name' by count
#order = counts.groupby('hpg_genre_name', observed=True)['n'].mean().sort_values().index
order = foobar.groupby('hpg_genre_name', observed=True)['n'].mean().sort_values(ascending=False).index


plt.figure(figsize=(8, 6))

# Create the boxplot with jitter
sns.boxplot(data=foobar, y='hpg_genre_name', x='n', order=order, color='lightgrey')
sns.stripplot(data=foobar, y='hpg_genre_name', x='n', order=order, color='red', alpha=0.7)

# Set y-axis to log scale
#plt.yscale('log')

# Set labels and title
plt.xlabel('hpg genre')
plt.ylabel('Cases per hpg area')
plt.tick_params(axis='y', pad=0, labelsize=7)
# Rotate x-axis labels
#plt.xticks(rotation=45)

# Show the plot
plt.show()

# Compute 'foo'
foo = air_visits.merge(air_store, on='air_store_id', how='left')

# Compute 'bar'
bar = air_store.groupby(['air_genre_name', 'air_area_name'], observed=True).size().reset_index(name='n')

# Compute 'foobar' (Assuming 'hpg_store' DataFrame is available)
foobar = hpg_store.groupby(['hpg_genre_name', 'hpg_area_name'], observed=True).size().reset_index(name='n')

p3_data = (
    foo.groupby(['air_genre_name', 'air_area_name'], observed=True)
    .agg(mean_log_visit=('visitors', lambda x: x.apply(lambda x: np.log1p(x)).mean()))
    .reset_index()
    .merge(bar, left_on=['air_genre_name', 'air_area_name'], right_on=['air_genre_name', 'air_area_name'], how='left')
    .groupby('n', observed=True)
    .agg(
        mean_mlv=('mean_log_visit', 'mean'),
        sd_mlv=('mean_log_visit', 'std')
    )
    .fillna(0)
    .reset_index()
)
# Multiplot layout
fig = plt.figure(figsize=(10, 5))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

# Assign each plot to a specific position
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[1, :])

# Plot p1 and p2 side by side
sns.histplot(data=bar, x='n', color='blue', binwidth=1, ax=ax1)
ax1.set(xlabel='Air Genres per area', ylabel='Count')
sns.histplot(data=foobar, x='n', color='red', binwidth=1, ax=ax2)
ax1.set(xlabel='HPG Genres per area', ylabel='Count')
# Plot p3
p3 = sns.scatterplot(data=p3_data, x='n', y='mean_mlv', color='blue', s=40, ax=ax3)
p3.errorbar(p3_data['n'], p3_data['mean_mlv'], yerr=p3_data['sd_mlv'], fmt='o', color='blue', markersize=5, capsize=8)
p3.set(xlabel='Cases of identical Air genres per area', ylabel='Mean +/- SD of\n mean log1p visitors')

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show()

We will try another method of quantifying the distinctiveness of a restaurant by the distance to its neighbouring restaurants in the feature engineering section.

5.4 Reservations vs Visits

Next we will turn our attention to the reservation numbers in the air_reserve and hpg_reserve data sets. We have seen their time series and distributions back in Sections 4.2 and 4.3; now we will compare the reservation numbers to the actual visitor numbers.

For this, we compute the sum of reserve_visitors per day (i.e. the number of people reservations were made for) for each restaurant id and then join these summaries to the air_visitors file. In order to include the hpg reservations we need to use the store_ids data to join the hpg_store_ids from the hpg_reserve file to the corresponding air_store_ids:

foo <- air_reserve %>%
  mutate(visit_date = date(visit_datetime)) %>%
  group_by(air_store_id,visit_date) %>%
  summarise(reserve_visitors_air = sum(reserve_visitors))

## `summarise()` has grouped output by 'air_store_id'. You can override using the
## `.groups` argument.

bar <- hpg_reserve %>%
  mutate(visit_date = date(visit_datetime)) %>%
  group_by(hpg_store_id,visit_date) %>%
  summarise(reserve_visitors_hpg = sum(reserve_visitors)) %>%
  inner_join(store_ids, by = "hpg_store_id")

## `summarise()` has grouped output by 'hpg_store_id'. You can override using the
## `.groups` argument.

all_reserve <- air_visits %>%
  inner_join(foo, by = c("air_store_id", "visit_date")) %>%
  inner_join(bar, by = c("air_store_id", "visit_date")) %>%
  mutate(reserve_visitors = reserve_visitors_air + reserve_visitors_hpg)

Now we will plot the total reserve_visitor numbers against the actual visitor numbers for the air restaurants. We use a scatter plot to which we are adding marginal histograms via the ggMarginal function of the ggExtra package. The grey line shows \(reserve_visitors == visitors\) and the blue line is a linear fit:

p <- all_reserve %>%
  filter(reserve_visitors < 120) %>%
  ggplot(aes(reserve_visitors, visitors)) +
  geom_point(color = "black", alpha = 0.5) +
  geom_abline(slope = 1, intercept = 0, color = "grey60") +
  geom_smooth(method = "lm", color = "blue")
ggMarginal(p, type="histogram", fill = "blue", bins=50)

## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

We find:

• The histograms show that the reserve_visitors and visitors numbers peak below ~20 and are largely confined to the range below 100.

• The scatter points fall largely above the line of identity, indicating that there were more visitors that day than had reserved a table. This is not surprising, since a certain number of people will always be walk-in customers.

• A notable fraction of the points is below the line, which probably indicates that some people made a reservation but changed their mind and didn’t go. That kind of effect is probably to be expected and taking it into account will be one of the challenges in this competition.

• The linear fit suggests a trend in which larger numbers of reserve_visitors are more likely to underestimate the eventual visitor numbers. This is not surprising either, since I can imagine that it is more likely that (a) a large reservation is cancelled than (b) a large group of people walk in a restaurant without reservation.

Now we will break down the discrepancy between visitors - reserve_visitors over time, look at the overall histograms, and visualise the air_reserve vs hpg_reserve numbers separately. Here, the time series for air (blue) and hpg (red) are offset vertically by 150 and -250 (see the solid black baselines):

p1 <- all_reserve %>%
  ggplot(aes(visitors - reserve_visitors)) +
  geom_histogram(binwidth = 5, fill = "black") +
  coord_flip() +
  labs(x = "")

p2 <- all_reserve %>%
  ggplot(aes(visitors - reserve_visitors_air)) +
  geom_histogram(binwidth = 5, fill = "blue") +
  coord_flip() +
  labs(x = "")

p3 <- all_reserve %>%
  ggplot(aes(visitors - reserve_visitors_hpg)) +
  geom_histogram(binwidth = 5, fill = "red") +
  coord_flip() +
  labs(x = "")

p4 <- all_reserve %>%
  ggplot(aes(visit_date, visitors - reserve_visitors)) +
  geom_hline(yintercept = c(150, 0, -250)) +
  geom_line() +
  geom_line(aes(visit_date, visitors - reserve_visitors_air + 150), color = "blue") +
  geom_line(aes(visit_date, visitors - reserve_visitors_hpg - 250), color = "red") +
  ggtitle("Visitors - Reserved: all (black), air (blue), hpg (red)")

layout <- matrix(c(4,4,2,4,4,1,4,4,3),3,3,byrow=TRUE)
multiplot(p1, p2, p3, p4, layout=layout)

We find:

• The time series show significant scatter throughout the training time range. While the air (blue) and hpg (red) curves are predominantly above the baseline (i.e. more visitors than reservations), combining the two data sets brings the mean of the distribution closer to the zero line. This can also be seen in the corresponding histograms on the right side.

• We see the gap where there are no air reservations (compare Sect. 4.2). We could only look at the hpg reservations here (for which this gap does not exist, Sect. 4.3) but it appears safe to assume that they would follow the same trend and can be used as a proxy for the air reservations. Feel free to check this assumption for the gap.

• The (flipped) histograms in the 3 right panels are roughly aligned with the time series in the left panel for convenience of interpretation. They demonstrate how much the distributions are skewed towards larger visitor numbers than reserve_visitor numbers. We might see a mix here between two distributions: a (probably normal) spread due to cancellations plus a tail from walk-in visitors, which should follow a Poisson distribution.

Finally, let’s have a quick look at the impact of holidays on the discrepancy between reservations and visitors. We’ll be using overlapping density plots:

all_reserve %>%
  mutate(date = visit_date) %>%
  left_join(holidays, by = "date") %>%
  ggplot(aes(visitors - reserve_visitors, fill = holiday_flg)) +
  geom_density(alpha = 0.5)

We find:

• There are somewhat higher numbers of visitors compared to reservations on a holiday. The peaks are almost identical, but we see small yet clear differences towards larger numbers.

# Process 'air_reserve' data
foo = (
    air_reserve.assign(visit_date=air_reserve['visit_datetime'].dt.date)
    .groupby(['air_store_id', 'visit_date'], observed=True)
    .agg(reserve_visitors_air=('reserve_visitors', 'sum'))
    .reset_index()
)

# Process 'hpg_reserve' data
bar = (
    hpg_reserve.assign(visit_date=hpg_reserve['visit_datetime'].dt.date)
    .groupby(['hpg_store_id', 'visit_date'], observed=True)
    .agg(reserve_visitors_hpg=('reserve_visitors', 'sum'))
    .reset_index()
    .merge(store_ids, left_on='hpg_store_id', right_on='hpg_store_id', how='inner')
)

air_visits['visit_date'] = air_visits['visit_date'].dt.date
# Combine reservation data with 'air_visits'
all_reserve = (
    air_visits.merge(foo, left_on=['air_store_id', 'visit_date'], right_on=['air_store_id', 'visit_date'], how='inner')
    .merge(bar, left_on=['air_store_id', 'visit_date'], right_on=['air_store_id', 'visit_date'], how='inner')
    .assign(reserve_visitors=lambda x: x['reserve_visitors_air'] + x['reserve_visitors_hpg'])
)

# Filter the data
filtered_data = all_reserve[all_reserve['reserve_visitors'] < 120]

fig = plt.figure(figsize=(10, 6))
plt.style.use('ggplot')
# Create the scatterplot with marginal histograms
g = sns.jointplot(x='reserve_visitors', y='visitors', data=filtered_data, color='blue', alpha=0.2, kind='scatter', palette='black')
g.plot_joint(sns.lineplot, color='grey')  # Add the diagonal line

## <seaborn.axisgrid.JointGrid object at 0x7f7efa54f1f0>

# Add a linear regression line
sns.regplot(x='reserve_visitors', y='visitors', data=filtered_data, ax=g.ax_joint, line_kws={'color': 'blue'})

# Add marginal histograms
plt.subplots_adjust(top=0.9)
g.fig.suptitle('Scatterplot with Marginal Histograms')

plt.show()

# Sort DataFrame by visit_date
all_reserve = all_reserve.sort_values(by='visit_date')

# Plot 1
plt.figure(figsize=(9, 6))
gs = GridSpec(3, 3)
plt.style.use('ggplot')


ax1 = plt.subplot(gs[0, 2])
ax1.hist(all_reserve['visitors'] - all_reserve['reserve_visitors'], 
        bins=range(-50, 60, 5), color='black', orientation='horizontal')
ax1.set_xlabel("")
ax1.invert_yaxis()
# Set size and rotation for x-axis tick labels
ax1.tick_params(axis='x', labelsize=8, rotation=0) 
ax1.tick_params(axis='y', labelsize=8, rotation=0)  

# Plot 2
ax2 = plt.subplot(gs[1, 2])
ax2.hist(all_reserve['visitors'] - all_reserve['reserve_visitors_air'],
         bins=range(-50, 60, 5), color='blue', orientation='horizontal')
ax2.set_xlabel("")
ax2.invert_yaxis()
# Set size and rotation for x-axis tick labels
ax2.tick_params(axis='x', labelsize=8, rotation=0)
ax2.tick_params(axis='y', labelsize=8, rotation=0)  

# Plot 3
ax3 = plt.subplot(gs[2, 2])
ax3.hist(all_reserve['visitors'] - all_reserve['reserve_visitors_hpg'],
         bins=range(-50, 60, 5), color='red', orientation='horizontal')
ax3.set_xlabel("")
ax3.invert_yaxis()
# Set size and rotation for x-axis tick labels
ax3.tick_params(axis='x', labelsize=8, rotation=0)  
ax3.tick_params(axis='y', labelsize=8, rotation=0)
ax3.set(xlabel='count') # ylabel='Count'

# Plot 4
ax4 = plt.subplot(gs[0:3, 0:2])
#ax4.axhline(y=[-300, 0, 300], color=['red', 'black', 'blue'], linestyle='--')
ax4.plot(all_reserve['visit_date'], 
        all_reserve['visitors'] - all_reserve['reserve_visitors'], color='black')
ax4.plot(all_reserve['visit_date'], 
        all_reserve['visitors'] - all_reserve['reserve_visitors_air'] + 150, color='blue')
ax4.plot(all_reserve['visit_date'], 
         all_reserve['visitors'] - all_reserve['reserve_visitors_hpg'] - 250, color='red')
ax4.set_title("Visitors - Reserved: all (black), air (blue), hpg (red)", fontsize=10)
# Format the x-axis date labels
ax4.xaxis.set_major_locator(mdates.MonthLocator(interval=3))
ax4.xaxis.set_major_formatter(mdates.DateFormatter('%Y-%m'))
# Set size and rotation for x-axis tick labels
ax4.tick_params(axis='x', labelsize=8, rotation=0)
ax4.set(xlabel='visit_date', ylabel= "visitors - reserve_visitors")


# Adjust layout
plt.tight_layout()

# Show the plot
plt.show()

# Convert visit_date to datetime if needed
all_reserve['visit_date'] = pd.to_datetime(all_reserve['visit_date'])
# Rename 'visit_date' column before merging
all_reserve['date'] = all_reserve['visit_date']

# Left join with holidays
reserve_holy = all_reserve.merge(holidays, on='date', how='left')

# Create the density plot
#sns.set(style="whitegrid")
plt.figure(figsize=(10, 6))
plt.style.use('ggplot')

sns.histplot(data=reserve_holy, x=(reserve_holy['visitors'] - reserve_holy['reserve_visitors']),
             kde=True, #kde_kws={'bw_method': 1},
             hue='holiday_flg', fill=True, alpha=0.5, palette='Set1')

plt.title("Density Plot of Visitors - Reserve Visitors")
plt.xlabel("Visitors - Reserve Visitors")
plt.ylabel("Density")
#plt.legend(loc='lower left')

plt.show()

6 Feature Engineering

The next step is to derive new features from the existing ones and the purpose of these new features is to provide additional predictive power for our goal to forecast visitor numbers. Those new features can be as simple as deriving the day of the week or the month from a date column; something that we have already used in Fig. 1 of our visual exploration. Or they can take a more complex shape from the interplay of several related variables. This section collects and studies these new features.

My personal preference is to collect all engineered features into a single code block, so that we don’t have to search for them in different places of the kernel. Often, this also makes the computation of these features easier as we can re-use certain intermediate transformations. As we expand our analysis, we will come back to this code block and it will grow as our feature space grows:

air_visits <- air_visits %>%
  mutate(wday = wday(visit_date, label=TRUE, week_start = 1),
         wday = fct_relevel(wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")),
         month = month(visit_date, label=TRUE))

air_reserve <- air_reserve %>%
  mutate(reserve_date = date(reserve_datetime),
         reserve_hour = hour(reserve_datetime),
         reserve_wday = wday(reserve_datetime, label = TRUE, week_start = 1),
         reserve_wday = fct_relevel(reserve_wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")),
         visit_date = date(visit_datetime),
         visit_hour = hour(visit_datetime),
         visit_wday = wday(visit_datetime, label = TRUE, week_start = 1),
         visit_wday = fct_relevel(visit_wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")),
         diff_hour = time_length(visit_datetime - reserve_datetime, unit = "hour"),
         diff_day = time_length(visit_datetime - reserve_datetime, unit = "day"))

hpg_reserve <- hpg_reserve %>%
  mutate(reserve_date = date(reserve_datetime),
         reserve_hour = hour(reserve_datetime),
         reserve_wday = wday(reserve_datetime, label = TRUE, week_start = 1),
         reserve_wday = fct_relevel(reserve_wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")),
         visit_date = date(visit_datetime),
         visit_hour = hour(visit_datetime),
         visit_wday = wday(visit_datetime, label = TRUE, week_start = 1),
         visit_wday = fct_relevel(visit_wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")),
         diff_hour = time_length(visit_datetime - reserve_datetime, unit = "hour"),
         diff_day = time_length(visit_datetime - reserve_datetime, unit = "day"))

# count stores in area
air_count <- air_store %>%
  group_by(air_area_name) %>%
  summarise(air_count = n())

hpg_count <- hpg_store %>%
  group_by(hpg_area_name) %>%
  summarise(hpg_count = n())

# distances
med_coord_air <- air_store %>%
  summarise_at(vars(longitude:latitude), median)
med_coord_hpg <- hpg_store %>%
  summarise_at(vars(longitude:latitude), median)

air_coords <- air_store %>%
  select(longitude, latitude)
hpg_coords <- hpg_store %>%
  select(longitude, latitude)

air_store$dist <- distCosine(air_coords, med_coord_air)/1e3
hpg_store$dist <- distCosine(hpg_coords, med_coord_hpg)/1e3

# apply counts, dist; add prefecture
air_store <- air_store %>%
  mutate(dist_group = as.integer(case_when(
    dist < 80 ~ 1,
    dist < 300 ~ 2,
    dist < 500 ~ 3,
    dist < 750 ~ 4,
    TRUE ~ 5))) %>%
  left_join(air_count, by = "air_area_name") %>%
  separate(air_area_name, c("prefecture"), sep = " ", remove = FALSE)

## Warning: Expected 1 pieces. Additional pieces discarded in 829 rows [1, 2, 3, 4, 5, 6,
## 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...].

hpg_store <- hpg_store %>%
  mutate(dist_group = as.integer(case_when(
    dist < 80 ~ 1,
    dist < 300 ~ 2,
    dist < 500 ~ 3,
    dist < 750 ~ 4,
    TRUE ~ 5))) %>%
  left_join(hpg_count, by = "hpg_area_name") %>%
  separate(hpg_area_name, c("prefecture"), sep = " ", remove = FALSE)

## Warning: Expected 1 pieces. Additional pieces discarded in 4690 rows [1, 2, 3, 4, 5, 6,
## 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...].

from pandas.api.types import CategoricalDtype

# Convert visit_date to datetime
air_visits['visit_date'] = pd.to_datetime(air_visits['visit_date'])

# Extract weekday
air_visits['wday'] = air_visits['visit_date'].dt.day_name()

# Reorder weekdays
weekday_order = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']
air_visits['wday'] = air_visits['wday'].astype(CategoricalDtype(categories=weekday_order, ordered=True))

# Extract month
air_visits['month'] = air_visits['visit_date'].dt.month_name()

# Convert visit_datetime to datetime
air_reserve['reserve_datetime'] = pd.to_datetime(air_reserve['reserve_datetime'])
air_reserve['visit_datetime'] = pd.to_datetime(air_reserve['visit_datetime'])

# Extract various date and time components
air_reserve['reserve_date'] = air_reserve['reserve_datetime'].dt.date
air_reserve['reserve_hour'] = air_reserve['reserve_datetime'].dt.hour
air_reserve['reserve_wday'] = air_reserve['reserve_datetime'].dt.day_name()
air_reserve['reserve_wday'] = air_reserve['reserve_wday'].astype(CategoricalDtype(categories=weekday_order, ordered=True))

air_reserve['visit_date'] = air_reserve['visit_datetime'].dt.date
air_reserve['visit_hour'] = air_reserve['visit_datetime'].dt.hour
air_reserve['visit_wday'] = air_reserve['visit_datetime'].dt.day_name()
air_reserve['visit_wday'] = air_reserve['visit_wday'].astype(CategoricalDtype(categories=weekday_order, ordered=True))

# Calculate time differences
air_reserve['diff_hour'] = (air_reserve['visit_datetime'] - air_reserve['reserve_datetime']).dt.total_seconds() / 3600
#air_reserve['diff_day'] = (air_reserve['visit_datetime'].dt.date - air_reserve['reserve_datetime'].dt.date)#.dt.days
air_reserve['diff_day'] = (air_reserve['visit_datetime'] - air_reserve['reserve_datetime']).apply(lambda x: x.total_seconds() / 86400)
# Count stores in area
air_count = air_store.groupby('air_area_name', observed=True).size().reset_index(name='air_count')

hpg_count = hpg_store.groupby('hpg_area_name', observed=True).size().reset_index(name='hpg_count')

# Calculate distances
med_coord_air = air_store[['longitude', 'latitude']].median()

med_coord_hpg = hpg_store[['longitude', 'latitude']].median()

air_coords = air_store[['longitude', 'latitude']]
hpg_coords = hpg_store[['longitude', 'latitude']]

air_store['dist'] = ((air_coords - med_coord_air)**2).sum(axis=1).pow(0.5) / 1000
hpg_store['dist'] = ((hpg_coords - med_coord_hpg)**2).sum(axis=1).pow(0.5) / 1000

# Apply counts, dist; add prefecture
def dist_group(x):
    if x < 80:
        return 1
    elif x < 300:
        return 2
    elif x < 500:
        return 3
    elif x < 750:
        return 4
    else:
        return 5

air_store['dist_group'] = air_store['dist'].apply(dist_group)
air_store = pd.merge(air_store, air_count, 
           left_on='air_area_name', right_on='air_area_name',
           how='left')
# Split 'air_area_name' into 'prefecture' and 'area'
split_data = air_store['air_area_name'].str.split(' ', n=1, expand=True)
# Assign the first part to 'prefecture' and the rest to 'area'
air_store['prefecture'] = split_data[0]
air_store['area'] = split_data[1]
# If there was only one part (no space), assign an empty string to 'area'
air_store['area'].fillna("", inplace=True)



hpg_store['dist_group'] = hpg_store['dist'].apply(dist_group)
hpg_store = pd.merge(hpg_store, hpg_count, 
                    left_on='hpg_area_name', 
                    right_on='hpg_area_name', 
                    how='left')

# Split 'air_area_name' into 'prefecture' and 'area'
split_data = hpg_store['hpg_area_name'].str.split(' ', n=1, expand=True)
# Assign the first part to 'prefecture' and the rest to 'area'
hpg_store['prefecture'] = split_data[0]
hpg_store['area'] = split_data[1]
# If there was only one part (no space), assign an empty string to 'area'
hpg_store['area'].fillna("", inplace=True)

6.1 Days of the week & months of the year

We start simple, with the week day (wday) and month features derived from the visit_date. We already looked at the total visitors per week day and month in Fig. 1. Now we will study the log1p transformed visitor numbers. We compute their mean and standard deviation and plot them alongside the (ridgeline) density distributions:

p1 <- air_visits %>%
  group_by(wday) %>%
  summarise(mean_log_visitors = mean(log1p(visitors)),
            sd_log_visitors = sd(log1p(visitors))) %>%
  ggplot(aes(wday, mean_log_visitors, color = wday)) +
  geom_point(size = 4) +
  geom_errorbar(aes(ymin = mean_log_visitors - sd_log_visitors,
                    ymax = mean_log_visitors + sd_log_visitors,
                    color = wday), width = 0.5, size = 0.7) +
  theme(legend.position = "none")

p2 <- air_visits %>%
  mutate(visitors = log1p(visitors)) %>%
  ggplot(aes(visitors, wday, fill = wday)) +
  geom_density_ridges(bandwidth = 0.1) +
  scale_x_log10() +
  theme(legend.position = "none") +
  labs(x = "log1p(visitors)", y = "")

p3 <- air_visits %>%
  group_by(month) %>%
  summarise(mean_log_visitors = mean(log1p(visitors)),
            sd_log_visitors = sd(log1p(visitors))) %>%
  ggplot(aes(month, mean_log_visitors, color = month)) +
  geom_point(size = 4) +
  geom_errorbar(aes(ymin = mean_log_visitors - sd_log_visitors,
                    ymax = mean_log_visitors + sd_log_visitors,
                    color = month), width = 0.5, size = 0.7) +
  theme(legend.position = "none")

p4 <- air_visits %>%
  mutate(visitors = log1p(visitors)) %>%
  ggplot(aes(visitors, month, fill = month)) +
  geom_density_ridges(bandwidth = 0.1) +
  scale_x_log10() +
  theme(legend.position = "none") +
  labs(x = "log1p(visitors)", y = "")

layout <- matrix(c(1,2,3,4),2,2,byrow=TRUE)
multiplot(p1, p2, p3, p4, layout=layout)

We find:

• The differences in mean log(visitor) numbers between the days of the week are much smaller than the corresponding uncertainties. This is confirmed by the density plots that show a strong overlap. Still, there is a trend toward higher visitor numbers on the weekend that might be useful.

• The months are even more similar, including the sligthly increased numbers in December. Overall, there is not much difference.

# Compute log1p of visitors
air_visits['log1p_visitors'] = air_visits['visitors'].apply(lambda x: np.log1p(x))
# Plot 1 data
p1_data = air_visits.groupby('wday', observed=True).agg(mean_log_visitors=('log1p_visitors', 'mean'), 
                                        sd_log_visitors=('log1p_visitors', 'std')).reset_index()

p3_data = air_visits.groupby('month', observed=True).agg(mean_log_visitors=('log1p_visitors', 'mean'), 
                                          sd_log_visitors=('log1p_visitors', 'std')).reset_index()


# Create a 2x2 grid
fig, axes = plt.subplots(1, 2, figsize=(10, 6))
plt.style.use('ggplot')

# Define custom order for weekdays and months
custom_wday_order = ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]
custom_month_order = ["Jan", "Feb", "Mar", "Apr", "May", "Jun", 
                      "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]

# Plot 1
p1 = sns.scatterplot(data=p1_data, x='wday', y='mean_log_visitors', 
                     hue='wday', #palette='viridis', 
                     ax=axes[0])
p1.errorbar(p1_data['wday'], p1_data['mean_log_visitors'],
            yerr=p1_data['sd_log_visitors'], fmt='o', 
            color='black',
            markersize=5,capsize=8)
# Set custom order for x-axis labels
#p1.xaxis.set_ticks(custom_wday_order)            
p1.set_xticklabels(custom_wday_order)  
p1.legend('')



# Plot 3
p3 = sns.scatterplot(data=p3_data, x='month', y='mean_log_visitors', 
                      hue='month', #palette='viridis',
                      ax=axes[1]) 
p3.errorbar(p3_data['month'], p3_data['mean_log_visitors'], 
            yerr=p3_data['sd_log_visitors'], 
            fmt='o', 
            color='black',
            #palette='viridis',
            markersize=5,capsize=8)
# Set custom order for x-axis labels
#p3.xaxis.set_ticks(custom_month_order)
p3.set_xticklabels(custom_month_order, rotation=45)  
p3.legend('')

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show()

# Plot 2
p2_data = air_visits.copy()
p2_data['log1p_visitors'] = p2_data['visitors'].apply(lambda x: np.log1p(x))

fig = plt.figure(figsize=(12, 12))

g = sns.FacetGrid(p2_data, 
                 row='wday', 
                 hue="wday", palette='viridis',
                 aspect=15, height=.5
                 )
p2= g.map(sns.kdeplot, 'log1p_visitors',
      bw_adjust=.5, clip_on=False,
      fill=True, alpha=1, linewidth=.5)
      
p2= g.map(sns.kdeplot, 'log1p_visitors', clip_on=False, color="black", lw=2, bw_adjust=.5)

# Define and use a simple function to label the plot in axes coordinates
def label(x, color, label):
    ax = plt.gca()
    ax.text(0, .2, label,  color=color, #fontweight="bold",
            ha="right", va="center", transform=ax.transAxes)

p2= g.map(label, 'log1p_visitors')

p2= g.set(xlim=(0, 10))
p2= g.set_titles("")
p2= g.set(yticks=[], ylabel="")
p2= g.despine(bottom=True, left=True)
p2= g.fig.subplots_adjust(hspace=-.25)

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show(p2)

# Plot 4
p4_data = air_visits.copy()
p4_data['log1p_visitors'] = p4_data['visitors'].apply(lambda x: np.log1p(x))

fig = plt.figure(figsize=(20, 20))

g = sns.FacetGrid(p2_data, 
                 row='month', 
                 hue="month", palette='viridis',
                 aspect=15, height=.5
                 )
p4= g.map(sns.kdeplot, 'log1p_visitors',
      bw_adjust=.5, clip_on=False,
      fill=True, alpha=1, linewidth=.5)
      
p4= g.map(sns.kdeplot, 'log1p_visitors', clip_on=False, color="black", lw=2, bw_adjust=.5)

# Define and use a simple function to label the plot in axes coordinates
def label(x, color, label):
    ax = plt.gca()
    ax.text(0, .2, label,  color=color, #fontweight="bold",
            ha="right", va="center", transform=ax.transAxes)

p4= g.map(label, 'log1p_visitors')

p4= g.set(xlim=(0, 10))
p4= g.set_titles("")
p4= g.set(yticks=[], ylabel="")
p4= g.despine(bottom=True, left=True)
p4= g.fig.subplots_adjust(hspace=-.25)

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show(p4)

import seaborn as sns
import matplotlib.pyplot as plt
import numpy as np

# Define a function to compute log1p of visitors
def compute_log1p_visitors(visitors):
    return np.log1p(visitors)

# Create subplots for p2 and p4
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(18, 12))
gs = GridSpec(3, 3)
plt.style.use('ggplot')
ax1 = plt.subplot(gs[0, 0])
ax2 = plt.subplot(gs[0, 1])

# Plot 2
p2_data = air_visits.copy()
p2_data['log1p_visitors'] = compute_log1p_visitors(p2_data['visitors'])

p2 = sns.FacetGrid(p2_data, row='wday', hue="wday", palette='viridis',
                 aspect=15, height=.5)
p2 =p2.map(sns.kdeplot, 'log1p_visitors', bw_adjust=.5, 
        clip_on=False, fill=True, alpha=1, linewidth=.5, ax=ax1)
p2= p2.map(sns.kdeplot, 'log1p_visitors', clip_on=False, color="black", lw=2, bw_adjust=.5, ax=ax1)
p2= p2.set(xlim=(0, 10))

# Define and use a simple function to label the plot in axes coordinates
def label(x, color, label):
    ax = plt.gca()
    ax.text(0, .2, label,  color=color, ha="right", va="center", transform=ax.transAxes)
p2= p2.map(label, 'log1p_visitors')

p2= p2.set_titles("")
p2= p2.set(yticks=[], ylabel="")
p2= p2.despine(bottom=True, left=True)
p2= p2.fig.subplots_adjust(hspace=-.25)

# Plot 4
p4_data = air_visits.copy()
p4_data['log1p_visitors'] = compute_log1p_visitors(p4_data['visitors'])

p4 = sns.FacetGrid(p4_data, row='month', hue="month", palette='viridis',
                 aspect=15, height=.5)
p4= p4.map(sns.kdeplot, 'log1p_visitors', bw_adjust=.5, 
       clip_on=False, fill=True, alpha=1,
       linewidth=.5, ax=ax2)
p4= p4.map(sns.kdeplot, 'log1p_visitors', clip_on=False, 
       color="black", lw=2, bw_adjust=.5, ax=ax2)
p4= p4.set(xlim=(0, 10))

p4= p4.map(label, 'log1p_visitors')

p4= p4.set_titles("")
p4= p4.set(yticks=[], ylabel="")
p4= p4.despine(bottom=True, left=True)
p4= p4.fig.subplots_adjust(hspace=-.25)

# Adjust layout
plt.tight_layout()

# Show the plots
plt.show()

Here is a breakdown by air_genre_name:

air_visits %>%
  left_join(air_store, by = "air_store_id") %>%
  group_by(wday, air_genre_name) %>%
  summarise(mean_log_visitors = mean(log1p(visitors)),
            sd_log_visitors = sd(log1p(visitors))) %>%
  ggplot(aes(wday, mean_log_visitors, color = wday)) +
  geom_point(size = 3) +
  geom_errorbar(aes(ymin = mean_log_visitors - sd_log_visitors,
                    ymax = mean_log_visitors + sd_log_visitors,
                    color = wday), width = 0.5, size = 0.7) +
  theme(legend.position = "none", axis.text.x  = element_text(angle=45, hjust=1, vjust=0.9)) +
  facet_wrap(~ air_genre_name)

## `summarise()` has grouped output by 'wday'. You can override using the
## `.groups` argument.

We find:

• There is a stronger impact of the weekend vs weekdays for genres such as “Karaoke” or “International Cuisine”, while others show very little change over the days of the week (e.g. “Japanese food”).

• Overall, there is no significant effect for any of the genres on any day of the week.

What about the statistics of visitors vs reservations? Does it depend on the day of the week? We use boxplots to find out:

all_reserve %>%
  mutate(wday = wday(visit_date, label=TRUE, week_start = 1),
         wday = fct_relevel(wday, c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"))) %>%
  ggplot(aes(wday, visitors - reserve_visitors, fill = wday)) +
  geom_boxplot() +
  theme(legend.position = "none")

We find that there is no significant difference, although we see a slight trend for more visitors compared to reservations on the weekend, especially Sunday.

from matplotlib import pyplot as plt, dates
locale.setlocale(locale.LC_ALL,'en_US.utf8')

## 'en_US.utf8'

# Compute log1p of visitors
air_visits['log1p_visitors'] = np.log1p(air_visits['visitors'])

# Merge air_visits and air_store
merged_data = pd.merge(air_visits, air_store, on='air_store_id', how='left')

# Group by wday and air_genre_name, compute mean and standard deviation
summary_data = merged_data.groupby(['wday', 'air_genre_name'], observed=True).agg(
    mean_log_visitors=('log1p_visitors', 'mean'),
    sd_log_visitors=('log1p_visitors', 'std')
).reset_index()


fig = plt.figure(figsize = (10,6))
plt.style.use('ggplot')

g = sns.FacetGrid(summary_data, col="air_genre_name", col_wrap=4,
                  sharex=True, sharey=True, height=5)
p = g.map_dataframe(sns.scatterplot, x='wday', y='mean_log_visitors',
                hue='wday', palette='viridis', s=50, alpha=0.7)

# Add error bars
for ax, (_, data) in zip(g.axes.flat, summary_data.groupby('air_genre_name')):
    #sns.lineplot(data=data, x='wday', y='mean_log_visitors', ax=ax, color='black')
    p= ax.errorbar(data['wday'], data['mean_log_visitors'], yerr=data['sd_log_visitors'], fmt='none', color='black', capsize=5)
    ax.legend('')

## <matplotlib.legend.Legend object at 0x7f7ef3a70a90>
## <matplotlib.legend.Legend object at 0x7f7f0bdd61d0>
## <matplotlib.legend.Legend object at 0x7f7f0bdd6a70>
## <matplotlib.legend.Legend object at 0x7f7f0bdd45b0>
## <matplotlib.legend.Legend object at 0x7f7f0bdd5ab0>
## <matplotlib.legend.Legend object at 0x7f7eef990070>
## <matplotlib.legend.Legend object at 0x7f7f0bdd6e60>
## <matplotlib.legend.Legend object at 0x7f7eefa22050>
## <matplotlib.legend.Legend object at 0x7f7eef991e70>
## <matplotlib.legend.Legend object at 0x7f7eefaffaf0>
## <matplotlib.legend.Legend object at 0x7f7efb56a6b0>
## <matplotlib.legend.Legend object at 0x7f7eef9dc310>
## <matplotlib.legend.Legend object at 0x7f7f0b322fe0>
## <matplotlib.legend.Legend object at 0x7f7eefa8f820>

# Resize facet titles
p= g.set_titles(col_template="{col_name}", 
               size = 8, backgroundcolor='#DDDDDD', pad=2
           # bbox={'facecolor': '#DDDDDD', 'alpha': 0, 'pad': 0}
            )
p= g.tick_params(axis='x', pad=0, labelsize= 6)
p= g.set_xlabels(fontsize=6, label="Date")
p= g.set_ylabels(fontsize=8 )#,label="Average number of visitors")

for ax in g.axes.flat:
    for label in ax.get_xticklabels():
        label.set_rotation(45)
        #ax.xaxis.set_major_formatter(dates.DateFormatter('%a'))

# Apply logarithmic scale to y-axis
#p= g.set(yscale="log")

# Set x-axis labels
p= g.set_axis_labels("Weekday", "Mean Log Visitors")
#p= g.add_legend(title="weekday")

# Adjust layout
p= plt.tight_layout()
# Show the plot
plt.show(p)

# Convert visit_date to datetime and extract the weekday
all_reserve['visit_date'] = pd.to_datetime(all_reserve['visit_date'])
all_reserve['wday'] = all_reserve['visit_date'].dt.day_name()

# Reorder the weekdays
weekday_order = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]
all_reserve['wday'] = pd.Categorical(all_reserve['wday'], categories=weekday_order, ordered=True)

#Create a new column for the difference between visitors and reserve_visitors
all_reserve['visitors_minus_reserve'] = all_reserve['visitors'] - all_reserve['reserve_visitors']

# Create the boxplot
plt.figure(figsize=(10, 6))

## <Figure size 1000x600 with 0 Axes>

plt.style.use('ggplot')

p= sns.boxplot(data=all_reserve, x='wday', y='visitors_minus_reserve', 
             hue='wday', palette='viridis')
p= plt.xlabel('Weekday')
p= plt.ylabel('Visitors - Reserve Visitors')
p= plt.tick_params(axis='x', pad=0, labelsize= 8)
#plt.set_major_formatter(dates.DateFormatter('%a'))
#plt.title('Difference between Visitors and Reserve Visitors by Weekday')

# Remove legend
#plt.legend().remove()
# Show the plot
plt.show(p)

6.2 Restaurant per area - air/hpg_count

This feature will address the question of how many restaurant can be found in a certain area and whether larger numbers of restaurants per area affect the average visitor numbers.

In order to compute it, we simply count the number of air/hpg restaurants for the corresponding areas. We show the resulting distributions in the next plot at the top. The we estimate the mean log1p-transformed visitor count per restaurant, and then compute the mean and standard deviation of this number for each area count group:

p1 <- air_count %>%
  ggplot(aes(air_count)) +
  geom_histogram(binwidth = 2, fill = "blue")

p2 <- hpg_count %>%
  ggplot(aes(hpg_count)) +
  geom_histogram(binwidth = 5, fill = "red")

p3 <- air_visits %>%
  left_join(air_store, by = "air_store_id") %>%
  group_by(air_store_id, air_count) %>%
  summarise(mean_store_visit = mean(log1p(visitors))) %>%
  group_by(air_count) %>%
  summarise(mean_log_visitors = mean(mean_store_visit),
            sd_log_visitors = sd(mean_store_visit)) %>%
  ggplot(aes(air_count, mean_log_visitors)) +
  geom_point(size = 4, color = "blue") +
  geom_errorbar(aes(ymin = mean_log_visitors - sd_log_visitors,
                    ymax = mean_log_visitors + sd_log_visitors),
                    color = "blue", width = 0.5, size = 0.7) +
  geom_smooth(method = "lm", color = "black") +
  labs(x = "Air restaurants per area")

## `summarise()` has grouped output by 'air_store_id'. You can override using the
## `.groups` argument.

layout <- matrix(c(1,2,3,3),2,2,byrow=TRUE)
multiplot(p1, p2, p3, layout=layout)

## `geom_smooth()` using formula = 'y ~ x'

We find:

• Most areas in the air data set have only a few restaurants, with the distribution peaking at 2. This goes back to the earlier observation that no single air_genre can ever be found in an air_area. There are always at least 2 of the same type. Still odd. The air data also has a tentative 2nd peak around 16-20. The hpg data, with larger overall numbers, also peaks at low counts and has few other, smaller peaks through its decline.

• The mean log1p visitor numbers per area have large uncertainties and are all consistent with each other. There is a slight trend, shown by the black linear regression, toward lower average numbers for larger areas but it is quite weak.

# Multiplot layout
fig = plt.figure(figsize=(9, 5))
gs = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[1, :])

# Plot 1
p1 = sns.histplot(data=air_count, x='air_count', 
                  bins=range(0, max(air_count['air_count'])+2, 2), 
                  color='blue',
                  ax=ax1
                  )
p1.set_xlabel('Air Count')

## Text(0.5, 0, 'Air Count')

p1.set_title('Air Count Histogram')

## Text(0.5, 1.0, 'Air Count Histogram')

# Plot 2
p2 = sns.histplot(data=hpg_count, x='hpg_count', 
                 bins=range(0, max(hpg_count['hpg_count'])+6, 5), 
                 color='red',
                 ax=ax2)
p2.set_xlabel('HPG Count')

## Text(0.5, 0, 'HPG Count')

p2.set_title('HPG Count Histogram')

## Text(0.5, 1.0, 'HPG Count Histogram')

# Preprocessing for Plot 3
air_visits_processed = air_visits.merge(air_store, on='air_store_id', how='left')

store_visits = air_visits_processed.groupby(['air_store_id', 'air_count'],
               observed=True)['visitors'].apply(lambda x: x.mean()).reset_index()
area_visits = store_visits.groupby('air_count', 
              observed=True)['visitors'].agg(['mean', 'std']).reset_index()


# Plot 3
p3 = sns.scatterplot(data=area_visits, x='air_count', y='mean',
                     color='blue',
                     ax=ax3)
p3= p3.errorbar(x=area_visits['air_count'], y=area_visits['mean'], 
            yerr=area_visits['std'], fmt='o',
            color='blue', capsize=5)
p3= sns.regplot(data=area_visits, x='air_count', y='mean', scatter=False, color='black', ax=ax3)

# Set labels and title for Plot 3
p3.set_xlabel('Air Restaurants per Area')

## Text(0.5, 0, 'Air Restaurants per Area')

p3.set_ylabel('Mean Log Visitors')

## Text(0, 0.5, 'Mean Log Visitors')

p3.set_title('Mean Log Visitors vs Air Restaurants per Area')

## Text(0.5, 1.0, 'Mean Log Visitors vs Air Restaurants per Area')

# Adjust layout
plt.tight_layout()
# Show the plots
plt.show()

6.3 Distance from the busiest area

Whenever we have spatial coordinates in our data we automatically also have the distances between these coordinates. As a first approximation we use the linear distance between two points (i.e. as the crow flies).

To compute these distances we are using the distCosine function of the geosphere package for spherical trigonometry. This method gives us the shortest distance between two points on a spherical earth. For the purpose of this localised analysis we choose to ignore ellipsoidal distortion of the earth’s shape.

As the single reference point for all distances we choose the median latitude and median longitude. Our analysis can be extended to investigate all the pairwise distances between two restaurants with the same methodology. We won’t perform this study in our kernel, but I encourage anyone who wants to try it to see whether additional insight can be gained this way.

Here, we plot the histograms of the distances from the medians for all the restaurants in the air and hpg data. These distributions will suggest a grouping into 5 different bins with ranges of increasing distance. We then compute the mean log1p visitor numbers for the 5 groups and compare them:

foo <- air_store %>% select(latitude, longitude, dist_group) %>% mutate(dset = "air")
bar <- hpg_store %>% select(latitude, longitude, dist_group) %>% mutate(dset = "hpg")

leaflet(foo) %>%
  addTiles() %>%
  addProviderTiles("CartoDB.Positron") %>%
  addScaleBar() %>%
  addCircleMarkers(~longitude, ~latitude, group = "AIR",
                   color = "blue", fillOpacity = 0.5, radius = 3*foo$dist_group) %>%
  addCircleMarkers(lng = bar$longitude, lat = bar$latitude, group = "HPG",
                   color = "red", fillOpacity = 0.5, radius = 3*bar$dist_group) %>%
  addCircleMarkers(lng = med_coord_air$longitude, lat = med_coord_air$latitude, group = "Centre",
                   color = "darkgreen", fillOpacity = 1) %>%
  addLayersControl(
    overlayGroups = c("AIR", "HPG", "Centre"),
    options = layersControlOptions(collapsed = FALSE)
  )

foo = air_store[['latitude', 'longitude', 'dist_group']].assign(dset='air')
bar = hpg_store[['latitude', 'longitude', 'dist_group']].assign(dset='hpg')
# Create a base map
m = folium.Map(location=[bar['latitude'].median(),
                         bar['longitude'].median()], 
                         zoom_start=5#,
                   #      tiles="CartoDB Positron",
             # attr="<a href=https://endless-sky.github.io/>Endless Sky</a>"
              )

# m = folium.Map(location=[35.647042153196615, 137.41531074957783], zoom_start=10,
#                tiles='https://{s}.basemaps.cartocdn.com/rastertiles/voyager_nolabels/{z}/{x}/{y}{r}.png', 
#                attr='CartoDB.Voyager', max_zoom=20)

# Add tiles
folium.TileLayer('CartoDB positron').add_to(m)

## <folium.raster_layers.TileLayer object at 0x7f7efa92cf70>

# Create a MarkerCluster object
marker_cluster = MarkerCluster().add_to(m)

#folium.LayerControl().add_to(m)
                  
# Define a function to add markers for hpg_store
def add_marker(row):
    folium.Marker(location=[row['latitude'], row['longitude']],
                  popup=row['hpg_store_id'],
                  icon=None,
                  tooltip=row['hpg_genre_name']).add_to(marker_cluster)

# Add markers for hpg_store
bar.apply(add_marker, axis=1)

## 'hpg_store_id'

# hpg_store.apply(lambda row:folium.Marker(
#                   location=[row['latitude'], row['longitude']],                        
#                   popup=row['hpg_store_id'],icon=None,
#                   tooltip=row['hpg_genre_name']).add_to(m), 
#                   axis=1)

# # Define a function to add markers for air_store
# def add_air_marker(row):
#     folium.Marker(location=[row['latitude'], row['longitude']],
#                   popup=row['air_store_id'],
#                   icon=None,
#                   tooltip=row['air_genre_name']).add_to(m)
                  
                  

# # Add markers for air_store
# air_store.apply(lambda row:folium.Marker(
#                   location=[row['latitude'], row['longitude']],
#                   popup=row['air_store_id'],
#                   icon=None,
#                   tooltip=row['air_genre_name']).add_to(m),
#                   axis=1)
# 
# # add a marker for med_coord_air
# folium.Marker(location=[35.658068, 139.685474],
#                    popup="Center Point",
#                    icon=folium.Icon(color='green'),
#                   tooltip="Center Point").add_to(m)

# Display the map
m

## <folium.folium.Map object at 0x7f7efa92e920>

6.4 Prefectures

This is a straight-forward feature where we simply define the prefecture as the first part of the area_name. Here we make use of the (generally) consistent formatting of the area name. This gives us a relatively small number of distinct high-level areas:

p1 <- air_store %>%
  ggplot(aes(prefecture)) +
  geom_bar(fill = "blue") +
  coord_flip() +
  ggtitle("air prefectures - # restaurants") +
  labs(x = "")

p2 <- hpg_store %>%
  ggplot(aes(prefecture)) +
  geom_bar(fill = "red") +
  coord_flip() +
  ggtitle("hpg prefectures - # restaurants") +
  labs(x = "")

p3 <- air_visits %>%
  left_join(air_store, by = "air_store_id") %>%
  group_by(air_store_id, prefecture) %>%
  summarise(mean_store_visit = mean(log1p(visitors))) %>%
  group_by(prefecture) %>%
  summarise(mean_log_visitors = mean(mean_store_visit),
            sd_log_visitors = sd(mean_store_visit)) %>%
  ggplot(aes(prefecture, mean_log_visitors)) +
  geom_point(size = 4, color = "blue") +
  geom_errorbar(aes(ymin = mean_log_visitors - sd_log_visitors,
                    ymax = mean_log_visitors + sd_log_visitors),
                    color = "blue", width = 0.5, size = 0.7) +
  labs(x = "prefecture") +
  theme(axis.text.x  = element_text(angle=15, hjust=1, vjust=0.9))

## `summarise()` has grouped output by 'air_store_id'. You can override using the
## `.groups` argument.

layout <- matrix(c(1,2,1,2,1,2,3,3,3,3),5,2,byrow=TRUE)
multiplot(p1, p2, p3, layout=layout)

We find:

• There are 9 prefectures in the air data and 13 entries in the hpg data. In both data sets “Tokyo” is clearly the most frequent entry.

• Once more, we don’t see signficant differences in the mean log1p visitor numbers for the 9 different air prefectures. Any possible variation is smaller than the size of the error bars.

# Create a 2x2 grid
fig = plt.figure(figsize=(8, 5))
grid = GridSpec(2, 2, figure=fig)
plt.style.use('ggplot')

# Plot 1 (p1)
p1_ax = fig.add_subplot(grid[0, 0])
air_store['prefecture'].value_counts().plot(kind='barh', color='blue', ax=p1_ax)

## <Axes: ylabel='prefecture'>

p1_ax.set_title('air prefectures - restaurants', fontsize= 10)

## Text(0.5, 1.0, 'air prefectures - restaurants')

p1_ax.set_xlabel('count')

## Text(0.5, 0, 'count')

p1_ax.tick_params(axis='y', rotation=0, labelsize= 6)
p1_ax.set_ylabel('')

## Text(0, 0.5, '')

# Plot 2 (p2)
p2_ax = fig.add_subplot(grid[0, 1])
hpg_store['prefecture'].value_counts().plot(kind='barh', color='red', ax=p2_ax)

## <Axes: ylabel='prefecture'>

p2_ax.set_title('hpg prefectures - restaurants', fontsize= 10)

## Text(0.5, 1.0, 'hpg prefectures - restaurants')

p2_ax.set_xlabel('count')

## Text(0.5, 0, 'count')

p2_ax.tick_params(axis='y', rotation=0, labelsize= 6)
p2_ax.set_ylabel('')

## Text(0, 0.5, '')

# Plot 3 (p3)
p3_data = (
    air_visits
    .merge(air_store, on='air_store_id')
    .groupby(['air_store_id', 'prefecture'])['visitors']
    .mean()
    .groupby('prefecture')
    .agg(mean_store_visit='mean', sd_log_visitors='std')
    .reset_index()
)

p3_ax = fig.add_subplot(grid[1, :])
p3_ax.errorbar(
    p3_data['prefecture'], p3_data['mean_store_visit'], yerr=p3_data['sd_log_visitors'],
    color='blue', marker='o', linestyle='-', capsize=5
)

## <ErrorbarContainer object of 3 artists>

p3_ax.set_title('Mean Store Visits by Prefecture', fontsize= 10)

## Text(0.5, 1.0, 'Mean Store Visits by Prefecture')

p3_ax.set_xlabel('Prefecture', fontlsize= 8)

## 'Text' object has no property 'fontlsize'

p3_ax.set_ylabel('Mean Store Visit', fontsize= 7)

## Text(0, 0.5, 'Mean Store Visit')

p3_ax.tick_params(axis='x', rotation=15, labelsize= 7)  # Customize x-axis ticks

# Adjust layout
fig.tight_layout()

# Show the plots
plt.show()

7 Time series parameters

After engineering new features based on the geographical or culinary properties of the different restaurants, we will now look directly at the time series of their visitor numbers. With only 829 time series, from 829 air restaurants, it is actually easily possible to look at each of them individually, and there are kernels that plot small or large fractions of them to get a feeling for the data.

Here, we will take a different approach and look at the meta parameters of each time series. Those features are the mean, standard deviation, slope, and, slope error of the time series. Each parameter is computed for the log1p-transformed data. In the next code block, we define a extraction function and then run it for each restaurant. Due to the small size of the data set this takes almost no time:

foo <- air_visits %>%
  left_join(air_store, by = "air_store_id") %>%
  group_by(air_store_id, air_genre_name) %>%
  summarise(mean_log_visits = mean(log1p(visitors)),
            mean_log_visits = mean(log1p(visitors)),
            sd_log_visits = sd(log1p(visitors))) %>%
  ungroup()

## `summarise()` has grouped output by 'air_store_id'. You can override using the
## `.groups` argument.

params_ts1 <- function(rownr){
  bar <- air_visits %>%
    filter(air_store_id == foo$air_store_id[rownr])
  slope <- summary(lm(visitors ~ visit_date, data = bar))$coef[2]
  slope_err <- summary(lm(visitors ~ visit_date, data = bar))$coef[4]
  
  foobar <- tibble(
    air_store_id = foo$air_store_id[rownr],
    slope = slope,
    slope_err = slope_err
  )
  
  return(foobar)
}

params <- params_ts1(1)
for (i in seq(2,nrow(foo))){
  params <- bind_rows(params, params_ts1(i))
}

ts_params <- foo %>%
  left_join(params, by = "air_store_id")

This Python code performs the same operations as the provided R code. It defines a function params_ts1 to calculate the slope and standard error for each air_store_id, then iterates through the foo DataFrame to compute these parameters. Finally, it merges the parameters with foo to obtain ts_params.

import pandas as pd
from statsmodels.regression.linear_model import OLS
from statsmodels.tools import add_constant

# Merge air_visits with air_store
merged_df = pd.merge(air_visits, air_store, on='air_store_id')
# Group by air_store_id and air_genre_name and compute the required statistics
foo = merged_df.groupby(['air_store_id', 'air_genre_name'],observed=True)
               .agg(mean_log_visits=('visitors', lambda x: np.mean(np.log1p(x))),
                    sd_log_visits=('visitors', lambda x: np.std(np.log1p(x))))
               .reset_index()


# Define function to calculate slope and standard error
def params_ts1(air_store_id):
    bar = air_visits[air_visits['air_store_id'] == air_store_id]
    X = add_constant(range(len(bar['visit_date'])))
    model = OLS(bar['visitors'], X)
    results = model.fit()
    slope = results.params[1]
    slope_err = results.bse[1]
    
    foobar = pd.DataFrame({
        'air_store_id': [air_store_id],
        'slope': [slope],
        'slope_err': [slope_err]
    })
    
    return foobar

# Calculate parameters for all rows in foo
params = params_ts1(foo['air_store_id'].iloc[0])
for i in range(1, len(foo)):
    params = pd.concat([params, params_ts1(foo['air_store_id'].iloc[i])], 
                       ignore_index=True)

# Merge parameters with foo
ts_params = foo.merge(params, on='air_store_id', how='left')

## unexpected indent (<string>, line 9)

Now we will plot the parameters and their one-dimensional and two-dimensional distributions:

p1 <- ts_params %>%
  ggplot(aes(mean_log_visits)) +
  geom_histogram(bins = 50, fill = "blue")

p2 <- ts_params %>%
  ggplot(aes(sd_log_visits)) +
  geom_histogram(bins = 50, fill = "blue")

p3 <- ts_params %>%
  filter(slope < 0.5) %>%
  ggplot(aes(slope)) +
  geom_histogram(bins = 50, fill = "blue") +
  labs(x = "Slope < 0.5")

p4 <- ts_params %>%
  ggplot((aes(mean_log_visits, sd_log_visits))) +
  geom_point(size = 2, color = "blue")

p5 <- ts_params %>%
  ggplot((aes(slope, slope_err))) +
  geom_point(size = 2, color = "blue")

layout <- matrix(c(1,1,2,2,3,3,4,4,4,5,5,5),2,6,byrow=TRUE)
multiplot(p1, p2, p3, p4, p5, layout=layout)

We find:

• The distributions of the mean and standard deviation for the log1p-transformed visitor counts are relatively broad. I don’t think we can assume normality for either of them, although the distributions are relatively symmetric. The shape of the mean vs sd cloud in the lower left panel support the idea that there is a relation between the two features, with larger average visitor counts having a smaller variance.

• The slope distribution is narrow; centred on zero slope. The slope vs slope error plot in the lower right panel showcases that there are a few outliers with large slope errors and mostly high absolute slope values:

# Define plots
def plot_p1(ax):
    ax.hist(ts_params['mean_log_visits'], bins=50, color='blue')
    ax.set_title('Mean Log Visits', fontsize=10)
    ax.set_ylabel('Count', fontsize=10)

def plot_p2(ax):
    ax.hist(ts_params['sd_log_visits'], bins=50, color='blue')
    ax.set_title('Standard Deviation Log Visits', fontsize=10)

def plot_p3(ax):
    filtered_data = ts_params[ts_params['slope'] < 0.5]
    ax.hist(filtered_data['slope'], bins=50, color='blue')
    ax.set_title('Slope < 0.5', fontsize= 10)

def plot_p4(ax):
    ax.scatter(ts_params['mean_log_visits'], 
               ts_params['sd_log_visits'], color='blue', s=2)
    ax.set_xlabel('Mean Log Visits', fontsize=6)
    ax.set_ylabel('Sd_Log_Visits', fontsize=10)
    ax.tick_params(axis='y', rotation=0, labelsize= 7) 

def plot_p5(ax):
    ax.scatter(ts_params['slope'], ts_params['slope_err'], color='blue', s=2)
    ax.set_xlabel('Slope', fontsize=6)
    ax.set_ylabel('Slope Error', fontsize=6)
    ax.tick_params(axis='y', rotation=0, labelsize= 7) 

# Create a 2x6 grid
fig = plt.figure(figsize=(8, 4))
gs = GridSpec(2, 6)

# Plot each subplot
plot_p1(fig.add_subplot(gs[0, :2]))

## name 'ts_params' is not defined

plot_p2(fig.add_subplot(gs[0, 2:4]))

## name 'ts_params' is not defined

plot_p3(fig.add_subplot(gs[0, 4:]))

## name 'ts_params' is not defined

plot_p4(fig.add_subplot(gs[1, :3]))

## name 'ts_params' is not defined

plot_p5(fig.add_subplot(gs[1, 3:]))

## name 'ts_params' is not defined

# Adjust layout
plt.tight_layout()

# Show the plots
plt.show()

ts_params %>%
  filter(abs(slope) > 0.25) %>%
  select(air_store_id, air_genre_name, slope, slope_err)

## # A tibble: 5 × 4
##   air_store_id         air_genre_name                slope slope_err
##   <chr>                <fct>                         <dbl>     <dbl>
## 1 air_1c0b150f9e696a5f Okonomiyaki/Monja/Teppanyaki -0.305    0.217 
## 2 air_8110d68cc869b85e Izakaya                       0.382    0.0984
## 3 air_900d755ebd2f7bbd Italian/French                2.06     0.385 
## 4 air_965b2e0cf4119003 Izakaya                       0.277    0.0265
## 5 air_9c6787aa03a45586 Cafe/Sweets                   0.832    0.150

ts_params[abs(ts_params['slope']) > 0.25][['air_store_id', 'air_genre_name', 'slope', 'slope_err']]

## name 'ts_params' is not defined

Finally, we will have a comprehensive view at the relation between mean log1p visitors and the time series slope using a facet zoom view, as implemented in the ggforce package. Here, we will see the full space on the right side and the zoomed-in version on the left side. The zoom region is indicated on the right side with a darker shading. This view is perfect for situations like this, where a few extreme points would make it difficult to focus on the properties of the majority data cluster. The mean_log_visits and slope are plotted coloured by genre and with associated errorbars in grey:

ts_params %>%
  ggplot(aes(mean_log_visits, slope, color = air_genre_name)) +
  geom_errorbarh(aes(xmin = mean_log_visits - sd_log_visits,
                    xmax = mean_log_visits + sd_log_visits),
                    color = "grey70", size = 0.7) +
  geom_errorbar(aes(ymin = slope - slope_err,
                    ymax = slope + slope_err),
                    color = "grey70", size = 0.7) +
  geom_point() +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(nrow = 3, override.aes = list(size = 4))) +
  labs(color = "") +
  facet_zoom(y = (slope < 0.05 & slope > -0.1))

We find:

• There’s not a lot of genre clustering, although the three points with the lowest mean log1p visits are all dining bars, for what it’s worth. We find the slope outliers in the again in the overview plot and notice that all of them have large mean values.

• Both panels show an overall trend for larger slopes to be associated to higher means. This may not be surprising, since we use he absolute slope value with has more range for high visitor counts than for low ones. Feel free to plot the slope normalised by mean to see whether the effect persists.

The extreme values in this plot can now be studied in detail, and we will choose some of them as examples in our next section.

# Filter data
filtered_data = ts_params[(ts_params['slope'] < 0.05) & (ts_params['slope'] > -0.1)]

## name 'ts_params' is not defined

# Create the scatter plot with error bars
plt.figure(figsize=(8, 6))

## <Figure size 800x600 with 0 Axes>

p1= sns.scatterplot(x='mean_log_visits', y='slope', hue='air_genre_name', data=filtered_data)

## Could not interpret value `mean_log_visits` for `x`. An entry with this name
## does not appear in `data`.

p1.errorbar(x=filtered_data['mean_log_visits'], y=filtered_data['slope'], 
             xerr=filtered_data['sd_log_visits'], yerr=filtered_data['slope_err'], 
             fmt='none', color='grey', alpha=0.7, elinewidth=0.7)

## 'mean_log_visits'

# Set legend properties
p1=plt.legend('')
#plt.legend(title='Air Genre Name', loc='upper left', bbox_to_anchor=(1, 1), ncol=1, fontsize='small')

# Add facet zoom
ax = plt.gca()
axins = ax.inset_axes([0.6, 0.6, 0.35, 0.35])
p2= sns.scatterplot(x='mean_log_visits', y='slope', hue='air_genre_name', data=filtered_data, ax=axins)

## Could not interpret value `mean_log_visits` for `x`. An entry with this name
## does not appear in `data`.

p2=axins.set_xlim(-2, 2)
p2=axins.set_ylim(-1, 1)

# Set labels and title
p2= plt.xlabel('Mean Log Visits')
p2= plt.ylabel('Slope')
p2= plt.title('Scatter Plot with Error Bars and Facet Zoom')
p2= plt.legend('')

plt.show()

8 Forcasting methods and examples

Finally, we will turn our focus to time-series forecasting methods. We have already learnt a lot about our data set and it’s features. The following sections will introduce basic forecasting methods.

8.1 ARIMA / auto.arima

A popular method for forecasting is the autoregressive integrated moving average model; short ARIMA model. This kind of model consists of three building blocks which parametrised by the three indeces p, d, q as ARIMA(p, d, q):

• auto-regressive / p: we are using past data to compute a regression model for future data. The parameter p indicates the range of lags; e.g. ARIMA(3,0,0) includes t-1, t-2, and t-3 values in the regression to compute the value at t.

• integrated / d: this is a differencing parameter, which gives us the number of times we are subtracting the current and the previous values of a time series. Differencing removes the change in a time series in that it stabilises the mean and removes (seasonal) trends. This is necessary since computing the lags (e.g. difference between time t and time t-1) is most meaningful if large-scale trends are removed. A time series where the variance (or amount of variability) (and the autocovariance) are time-invariant (i.e. don’t change from day to day) is called stationary.

• moving average / q: this parameter gives us the number of previous error terms to include in the regression error of the model.

Here we will be using the auto.arima tool which estimates the necessary ARIMA parameters for each individual time series. In order to feed our data to auto.arima we need to turn them into a time-series object using the ts tool. We will also add a step for cleaning and outlier removal via the tsclean function of the forecast package. We have already seen that our data contain a strong weekly cycle, which will be one of the pre-set parameters of our model. We will include this knowledge when transforming our data. Let’s set everything up step by step, with comments and explanations, and then turn it into a function. Unhide the code to see how it is implemented.

We use the first air_store_id (“air_ba937bf13d40fb24”) as an example.

air_id = "air_ba937bf13d40fb24"

pred_len <- test %>%
  separate(id, c("air", "store_id", "date"), sep = "_") %>%
  distinct(date) %>%
  nrow()

air_id = "air_ba937bf13d40fb24"

# Separate the 'id' column into three columns
test[['air', 'store_id', 'date']] = test['id'].str.split('_', expand=True)

# Get distinct dates and calculate the number of rows
pred_len = test['date'].nunique()

We choose to predict for the last 39 days of our training sample. This might not be here we compute the upper end of our training dates and subtract our “prediction length” from this value to define the start of our validation sample on Mar 14th. We also create a data set of all visit_dates in preparation for many time series having gaps.

max_date <- max(air_visits$visit_date)
split_date <- max_date - pred_len
all_visits <- tibble(visit_date = seq(min(air_visits$visit_date), max(air_visits$visit_date), 1))

from datetime import timedelta
# Find the maximum visit date
max_date = air_visits['visit_date'].max()

# Calculate the split date
split_date = max_date - timedelta(days=pred_len)

# Create a DataFrame with a sequence of dates
all_visits = pd.DataFrame({'visit_date': pd.date_range(start=min(air_visits['visit_date']), end=max(air_visits['visit_date']))})

Next, we extract the time series for the specific air_store_id. We transform the visitors counts by log1p and join the data set of all visit_dates. This gives us a number of NA which we fill in with the overall median. The median might not be the best choice here, but it’s a sensible starting point. Most time series prediction tools require a sequential time series without gaps; which is what we create in this step.

foo <- air_visits %>%
  filter(air_store_id == air_id)

visits <- foo %>%
  right_join(all_visits, by = "visit_date") %>%
  mutate(visitors = log1p(visitors)) %>%
  replace_na(list(visitors = median(log1p(foo$visitors)))) %>%
  rownames_to_column()

# Assuming you have DataFrames 'air_visits', 'all_visits' available

#air_id = "air_900d755ebd2f7bbd"
# Filter air_visits for a specific air_store_id (assuming air_id is a variable)
foo = air_visits[air_visits['air_store_id'] == air_id] 

# Right join with all_visits on visit_date
visits = pd.merge(all_visits, foo, on='visit_date', how='right')

# Apply log transformation to visitors column
visits['visitors'] = np.log1p(visits['visitors'])

# Replace NA values with the median of log-transformed visitors from 'foo'
median_visitors = np.median(np.log1p(foo['visitors']))
visits['visitors'].fillna(median_visitors, inplace=True)

# Reset row indices
visits = visits.reset_index(drop=True)

Using this new time series, we now split the data into training and validation sets.

visits_train <- visits %>% filter(visit_date <= split_date)
visits_valid <- visits %>% filter(visit_date > split_date)

# Filter visits for training and validation sets based on visit_date
visits_train = visits[visits['visit_date'] <= split_date]
visits_valid = visits[visits['visit_date'] > split_date]

Now comes the fitting part. As said before, we use the ts function to create a time series object and the tsclean tool to remove outliers. We also add the weekly frequency. The stepwise and approximation parameter settings mean that the tool performs a more thorough and precise search over all model parameters. This increases the computing time, but for our small data set this doesn’t matter much.

arima.fit <- auto.arima(tsclean(ts(visits_train$visitors, frequency = 7)),
                        stepwise = FALSE, approximation = FALSE)

from pmdarima import auto_arima
from statsmodels.tsa.seasonal import seasonal_decompose

# Assuming 'visits_train' DataFrame is available

# Perform seasonal decomposition of time series
result = seasonal_decompose(visits_train['visitors'], model='multiplicative', period=7)

# Extract the trend component (you may need to adjust the index based on the result)
trend = result.trend.dropna()

visits_train.set_index('visit_date', inplace=True)
# Fit ARIMA model
arima_fit = auto_arima(trend.to_numpy(), seasonal=True, m=7, stepwise=False, trace=True) 

##  ARIMA(0,1,0)(0,0,0)[7] intercept   : AIC=-572.155, Time=0.06 sec
##  ARIMA(0,1,0)(0,0,1)[7] intercept   : AIC=-722.904, Time=0.46 sec
##  ARIMA(0,1,0)(0,0,2)[7] intercept   : AIC=inf, Time=2.85 sec
##  ARIMA(0,1,0)(1,0,0)[7] intercept   : AIC=-633.575, Time=0.28 sec
##  ARIMA(0,1,0)(1,0,1)[7] intercept   : AIC=inf, Time=1.15 sec
##  ARIMA(0,1,0)(1,0,2)[7] intercept   : AIC=-724.912, Time=2.12 sec
##  ARIMA(0,1,0)(2,0,0)[7] intercept   : AIC=-668.883, Time=0.88 sec
##  ARIMA(0,1,0)(2,0,1)[7] intercept   : AIC=inf, Time=3.14 sec
##  ARIMA(0,1,0)(2,0,2)[7] intercept   : AIC=inf, Time=3.88 sec
##  ARIMA(0,1,1)(0,0,0)[7] intercept   : AIC=-576.206, Time=0.10 sec
##  ARIMA(0,1,1)(0,0,1)[7] intercept   : AIC=-721.068, Time=1.29 sec
##  ARIMA(0,1,1)(0,0,2)[7] intercept   : AIC=inf, Time=4.03 sec
##  ARIMA(0,1,1)(1,0,0)[7] intercept   : AIC=-631.984, Time=0.46 sec
##  ARIMA(0,1,1)(1,0,1)[7] intercept   : AIC=inf, Time=1.65 sec
##  ARIMA(0,1,1)(1,0,2)[7] intercept   : AIC=-722.919, Time=3.20 sec
##  ARIMA(0,1,1)(2,0,0)[7] intercept   : AIC=-667.242, Time=1.91 sec
##  ARIMA(0,1,1)(2,0,1)[7] intercept   : AIC=inf, Time=3.68 sec
##  ARIMA(0,1,1)(2,0,2)[7] intercept   : AIC=inf, Time=8.54 sec
##  ARIMA(0,1,2)(0,0,0)[7] intercept   : AIC=-575.251, Time=0.23 sec
##  ARIMA(0,1,2)(0,0,1)[7] intercept   : AIC=-722.316, Time=1.52 sec
##  ARIMA(0,1,2)(0,0,2)[7] intercept   : AIC=-723.965, Time=5.41 sec
##  ARIMA(0,1,2)(1,0,0)[7] intercept   : AIC=-635.495, Time=0.83 sec
##  ARIMA(0,1,2)(1,0,1)[7] intercept   : AIC=inf, Time=2.15 sec
##  ARIMA(0,1,2)(1,0,2)[7] intercept   : AIC=-722.548, Time=6.39 sec
##  ARIMA(0,1,2)(2,0,0)[7] intercept   : AIC=-669.723, Time=1.99 sec
##  ARIMA(0,1,2)(2,0,1)[7] intercept   : AIC=-721.007, Time=3.82 sec
##  ARIMA(0,1,3)(0,0,0)[7] intercept   : AIC=-573.274, Time=0.19 sec
##  ARIMA(0,1,3)(0,0,1)[7] intercept   : AIC=-720.478, Time=2.26 sec
##  ARIMA(0,1,3)(0,0,2)[7] intercept   : AIC=-721.586, Time=6.54 sec
##  ARIMA(0,1,3)(1,0,0)[7] intercept   : AIC=-634.771, Time=1.05 sec
##  ARIMA(0,1,3)(1,0,1)[7] intercept   : AIC=-721.483, Time=2.68 sec
##  ARIMA(0,1,3)(2,0,0)[7] intercept   : AIC=-670.548, Time=3.44 sec
##  ARIMA(0,1,4)(0,0,0)[7] intercept   : AIC=-580.791, Time=0.70 sec
##  ARIMA(0,1,4)(0,0,1)[7] intercept   : AIC=-718.628, Time=3.37 sec
##  ARIMA(0,1,4)(1,0,0)[7] intercept   : AIC=-636.704, Time=1.29 sec
##  ARIMA(0,1,5)(0,0,0)[7] intercept   : AIC=-603.486, Time=1.18 sec
##  ARIMA(1,1,0)(0,0,0)[7] intercept   : AIC=-575.533, Time=0.08 sec
##  ARIMA(1,1,0)(0,0,1)[7] intercept   : AIC=-721.036, Time=0.73 sec
##  ARIMA(1,1,0)(0,0,2)[7] intercept   : AIC=inf, Time=3.59 sec
##  ARIMA(1,1,0)(1,0,0)[7] intercept   : AIC=-631.892, Time=0.60 sec
##  ARIMA(1,1,0)(1,0,1)[7] intercept   : AIC=inf, Time=1.38 sec
##  ARIMA(1,1,0)(1,0,2)[7] intercept   : AIC=-722.918, Time=4.28 sec
##  ARIMA(1,1,0)(2,0,0)[7] intercept   : AIC=-667.167, Time=1.81 sec
##  ARIMA(1,1,0)(2,0,1)[7] intercept   : AIC=inf, Time=4.38 sec
##  ARIMA(1,1,0)(2,0,2)[7] intercept   : AIC=inf, Time=5.82 sec
##  ARIMA(1,1,1)(0,0,0)[7] intercept   : AIC=-592.370, Time=0.21 sec
##  ARIMA(1,1,1)(0,0,1)[7] intercept   : AIC=-719.396, Time=1.71 sec
##  ARIMA(1,1,1)(0,0,2)[7] intercept   : AIC=inf, Time=4.90 sec
##  ARIMA(1,1,1)(1,0,0)[7] intercept   : AIC=-642.377, Time=1.31 sec
##  ARIMA(1,1,1)(1,0,1)[7] intercept   : AIC=inf, Time=2.24 sec
##  ARIMA(1,1,1)(1,0,2)[7] intercept   : AIC=-721.014, Time=6.09 sec
##  ARIMA(1,1,1)(2,0,0)[7] intercept   : AIC=-672.775, Time=3.93 sec
##  ARIMA(1,1,1)(2,0,1)[7] intercept   : AIC=inf, Time=4.67 sec
##  ARIMA(1,1,2)(0,0,0)[7] intercept   : AIC=-573.238, Time=0.17 sec
##  ARIMA(1,1,2)(0,0,1)[7] intercept   : AIC=-720.540, Time=2.07 sec
##  ARIMA(1,1,2)(0,0,2)[7] intercept   : AIC=-721.961, Time=6.39 sec
##  ARIMA(1,1,2)(1,0,0)[7] intercept   : AIC=-641.027, Time=1.54 sec
##  ARIMA(1,1,2)(1,0,1)[7] intercept   : AIC=inf, Time=2.25 sec
##  ARIMA(1,1,2)(2,0,0)[7] intercept   : AIC=-672.363, Time=4.64 sec
##  ARIMA(1,1,3)(0,0,0)[7] intercept   : AIC=-571.251, Time=0.51 sec
##  ARIMA(1,1,3)(0,0,1)[7] intercept   : AIC=-718.480, Time=2.66 sec
##  ARIMA(1,1,3)(1,0,0)[7] intercept   : AIC=-638.002, Time=1.70 sec
##  ARIMA(1,1,4)(0,0,0)[7] intercept   : AIC=-624.737, Time=1.07 sec
##  ARIMA(2,1,0)(0,0,0)[7] intercept   : AIC=-575.078, Time=0.10 sec
##  ARIMA(2,1,0)(0,0,1)[7] intercept   : AIC=-721.989, Time=1.09 sec
##  ARIMA(2,1,0)(0,0,2)[7] intercept   : AIC=-723.806, Time=4.07 sec
##  ARIMA(2,1,0)(1,0,0)[7] intercept   : AIC=-634.016, Time=0.90 sec
##  ARIMA(2,1,0)(1,0,1)[7] intercept   : AIC=inf, Time=1.73 sec
##  ARIMA(2,1,0)(1,0,2)[7] intercept   : AIC=-722.356, Time=4.64 sec
##  ARIMA(2,1,0)(2,0,0)[7] intercept   : AIC=-668.382, Time=2.65 sec
##  ARIMA(2,1,0)(2,0,1)[7] intercept   : AIC=-721.289, Time=5.42 sec
##  ARIMA(2,1,1)(0,0,0)[7] intercept   : AIC=-573.350, Time=0.19 sec
##  ARIMA(2,1,1)(0,0,1)[7] intercept   : AIC=-719.992, Time=1.70 sec
##  ARIMA(2,1,1)(0,0,2)[7] intercept   : AIC=inf, Time=5.30 sec
##  ARIMA(2,1,1)(1,0,0)[7] intercept   : AIC=-641.074, Time=1.96 sec
##  ARIMA(2,1,1)(1,0,1)[7] intercept   : AIC=inf, Time=2.08 sec
##  ARIMA(2,1,1)(2,0,0)[7] intercept   : AIC=-672.456, Time=5.68 sec
##  ARIMA(2,1,2)(0,0,0)[7] intercept   : AIC=inf, Time=0.47 sec
##  ARIMA(2,1,2)(0,0,1)[7] intercept   : AIC=-730.214, Time=2.35 sec
##  ARIMA(2,1,2)(1,0,0)[7] intercept   : AIC=inf, Time=2.36 sec
##  ARIMA(2,1,3)(0,0,0)[7] intercept   : AIC=-593.525, Time=1.09 sec
##  ARIMA(3,1,0)(0,0,0)[7] intercept   : AIC=-573.316, Time=0.15 sec
##  ARIMA(3,1,0)(0,0,1)[7] intercept   : AIC=-719.991, Time=1.79 sec
##  ARIMA(3,1,0)(0,0,2)[7] intercept   : AIC=-721.890, Time=4.84 sec
##  ARIMA(3,1,0)(1,0,0)[7] intercept   : AIC=-632.159, Time=1.26 sec
##  ARIMA(3,1,0)(1,0,1)[7] intercept   : AIC=-721.426, Time=2.57 sec
##  ARIMA(3,1,0)(2,0,0)[7] intercept   : AIC=-667.963, Time=3.19 sec
##  ARIMA(3,1,1)(0,0,0)[7] intercept   : AIC=-571.480, Time=0.30 sec
##  ARIMA(3,1,1)(0,0,1)[7] intercept   : AIC=-717.996, Time=2.20 sec
##  ARIMA(3,1,1)(1,0,0)[7] intercept   : AIC=-636.488, Time=2.33 sec
##  ARIMA(3,1,2)(0,0,0)[7] intercept   : AIC=inf, Time=0.54 sec
##  ARIMA(4,1,0)(0,0,0)[7] intercept   : AIC=-574.061, Time=0.19 sec
##  ARIMA(4,1,0)(0,0,1)[7] intercept   : AIC=-720.621, Time=1.35 sec
##  ARIMA(4,1,0)(1,0,0)[7] intercept   : AIC=-636.775, Time=1.81 sec
##  ARIMA(4,1,1)(0,0,0)[7] intercept   : AIC=-590.360, Time=0.96 sec
##  ARIMA(5,1,0)(0,0,0)[7] intercept   : AIC=-584.809, Time=0.67 sec
## 
## Best model:  ARIMA(2,1,2)(0,0,1)[7] intercept
## Total fit time: 223.510 seconds

Using the fitted ARIMA model we will forecast for our “prediction length”. We include confidence intervals.

arima_visits <- arima.fit %>% forecast(h = pred_len, level = c(50,95))

arima_visits %>%
  autoplot +
  geom_line(aes(as.integer(rowname)/7, visitors), data = visits_valid, color = "grey40") +
  labs(x = "Time [weeks]", y = "log1p visitors vs auto.arima predictions")

We find that the first days of the forecast fit quite well, but then our prediction is not able to capture the larger spikes. Still, it’s a useful starting point to compare other methods to.

# Generate forecasts
arima_forecast, conf_int = arima_fit.predict(n_periods=pred_len, return_conf_int=True)

# Convert the forecasts to a DataFrame with appropriate dates

forecast_dates = pd.date_range(start=split_date + pd.Timedelta(days=1), periods=pred_len)

arima_forecast_df = pd.DataFrame({
    'date': forecast_dates,
    'forecast': arima_forecast
})

# Optionally, add confidence intervals
arima_forecast_df['lower_conf_int'] = conf_int[:, 0]
arima_forecast_df['upper_conf_int'] = conf_int[:, 1]

# Plot the points and the forecasts
x_axis = np.arange(visits_train.shape[0] + arima_forecast.shape[0])
x_dates = visits['visit_date']  # Year starts at 1821

p= plt.plot(x_dates[x_axis[:visits_train.shape[0]]].to_numpy(), 
            visits_train['visitors'].to_numpy(), 
            alpha=0.75, color='black')
p= plt.plot(arima_forecast_df['date'].to_numpy(), 
            arima_forecast_df['forecast'].to_numpy(), 
            alpha=0.75, color='blue')  # Forecasts
p= plt.plot(visits_valid['visit_date'].to_numpy(), 
               visits_valid['visitors'],
               alpha=0.4, color='grey')  # valid data
#p= plt.scatter(visits_valid['visit_date'].to_numpy(), 
#               visits_valid['visitors'],
#               alpha=0.4, color='grey', marker='x')
p= plt.fill_between(arima_forecast_df['date'].to_numpy(),
                 arima_forecast_df['lower_conf_int'], 
                 arima_forecast_df['upper_conf_int'], 
                 alpha=0.2, color='b')
#p= plt.title("ARIMA forecasts")
p= plt.xlabel("dates")
p=plt.ylabel("log1p visitors vs auto.arima predictions")

plt.show(p)

Now we turn this procedure into a function, including the plotting part.

plot_auto_arima_air_id <- function(air_id){

  pred_len <- test %>%
    separate(id, c("air", "store_id", "date"), sep = "_") %>%
    distinct(date) %>%
    nrow()

  max_date <- max(air_visits$visit_date)
  split_date <- max_date - pred_len
  all_visits <- tibble(visit_date = seq(min(air_visits$visit_date), max(air_visits$visit_date), 1))
  
  foo <- air_visits %>%
    filter(air_store_id == air_id)

  visits <- foo %>%
    right_join(all_visits, by = "visit_date") %>%
    mutate(visitors = log1p(visitors)) %>%
    replace_na(list(visitors = median(log1p(foo$visitors)))) %>%
    rownames_to_column()
  
  visits_train <- visits %>% filter(visit_date <= split_date)
  visits_valid <- visits %>% filter(visit_date > split_date)

  arima.fit <- auto.arima(tsclean(ts(visits_train$visitors, frequency = 7)),
                          stepwise = FALSE, approximation = FALSE)

  arima_visits <- arima.fit %>% forecast(h = pred_len, level = c(50,95))

  arima_visits %>%
    autoplot +
    geom_line(aes(as.integer(rowname)/7, visitors), data = visits_valid, color = "grey40") +
    labs(x = "Time [weeks]", y = "log1p visitors vs forecast")
}

def plot_auto_arima_air_id(air_id, ax):
  
    # Separate the 'id' column into three columns
    test[['air', 'store_id', 'date']] = test['id'].str.split('_', expand=True)
    # Get distinct dates and calculate the number of rows
    pred_len = test['date'].nunique()
    # Find the maximum visit date
    max_date = air_visits['visit_date'].max()
  
    # Calculate the split date
    split_date = max_date - timedelta(days=pred_len)
  
    # Create a DataFrame with a sequence of dates
    all_visits = pd.DataFrame({'visit_date': pd.date_range(start=min(air_visits['visit_date']), end=max(air_visits['visit_date']))})
    
    # Filter air_visits for a specific air_store_id (assuming air_id is a variable)
    foo = air_visits[air_visits['air_store_id'] == air_id]
  
    # Right join with all_visits on visit_date
    visits = pd.merge(all_visits, foo, on='visit_date', how='right')
  
    # Apply log transformation to visitors column
    visits['visitors'] = np.log1p(visits['visitors'])
  
    # Replace NA values with the median of log-transformed visitors from 'foo'
    median_visitors = np.median(np.log1p(foo['visitors']))
    visits['visitors'].fillna(median_visitors, inplace=True)
  
    # Reset row indices
    visits = visits.reset_index(drop=True)
    # Filter visits for training and validation sets based on visit_date
    visits_train = visits[visits['visit_date'] <= split_date]
    visits_valid = visits[visits['visit_date'] > split_date]
    
    
    # Perform seasonal decomposition of time series
    result = seasonal_decompose(visits_train['visitors'], model='multiplicative', period=7)
  
    # Extract the trend component (you may need to adjust the index based on the result)
    trend = result.trend.dropna()
    visits_train.set_index('visit_date', inplace=True)
    
    # Fit ARIMA model
    arima_fit = auto_arima(trend.to_numpy(), seasonal=True, m=7, stepwise=False, trace=False)
    
    # Generate forecasts
    arima_forecast, conf_int = arima_fit.predict(n_periods=pred_len, return_conf_int=True)
  
    # Convert the forecasts to a DataFrame with appropriate dates
    forecast_dates = pd.date_range(start=split_date + pd.Timedelta(days=1), periods=pred_len)
  
    arima_forecast_df = pd.DataFrame({
      'date': forecast_dates,
      'forecast': arima_forecast
    })
  
    # Optionally, add confidence intervals
    arima_forecast_df['lower_conf_int'] = conf_int[:, 0]
    arima_forecast_df['upper_conf_int'] = conf_int[:, 1]
    
    # Plot the points and the forecasts
    x_axis = np.arange(visits_train.shape[0] + arima_forecast.shape[0])
    x_dates = visits['visit_date']
    
    fig, ax = plt.subplots(figsize=(8, 8))
    
    ax.plot(x_dates[x_axis[:visits_train.shape[0]]].to_numpy(), 
              visits_train['visitors'].to_numpy(), 
              alpha=0.75, color='black')
    ax.plot(arima_forecast_df['date'].to_numpy(), 
              arima_forecast_df['forecast'].to_numpy(), 
              alpha=0.75, color='blue')  # Forecasts
    ax.plot(visits_valid['visit_date'].to_numpy(), 
                 visits_valid['visitors'],
                 alpha=0.4, color='grey')  # valid data
    #ax.scatter(visits_valid['visit_date'].to_numpy(), 
    #               visits_valid['visitors'],
    #               alpha=0.4, color='grey', marker='x',
    #               ax=["ax" + str(axe)])
    ax.fill_between(arima_forecast_df['date'].to_numpy(),
                   arima_forecast_df['lower_conf_int'], 
                   arima_forecast_df['upper_conf_int'], 
                   alpha=0.2, color='b')
    #ax.plt.title("ARIMA forecasts")
    ax.tick_params(axis='x', rotation=45, labelsize= 7) 
    plt.xlabel("dates")
    plt.ylabel("log1p visitors vs auto.arima predictions")
    

And we apply this function to a few time series’, including two of the slope outliers from the previous section:

ranked_store <- air_visits %>%
                group_by('air_store_id') %>%
                summarize(N = sum(visitors)) %>%
                arrange(desc(N) )
p1 <- plot_auto_arima_air_id("air_f3f9824b7d70c3cf")
p2 <- plot_auto_arima_air_id("air_8e4360a64dbd4c50")
#p3 <- plot_auto_arima_air_id("air_399904bdb7685ca0")
#p4 <- plot_auto_arima_air_id("air_f26f36ec4dc5adb0")

#layout <- matrix(c(1,2,3,4),2,2,byrow=TRUE)
layout <- matrix(c(1,2),1,2,byrow=TRUE)
multiplot(p1, p2, layout=layout)

We find:

• The two time series’ in the upper panels are reasonable complete, but we see that the long gaps (and our median filling) lead to problems in the predictions in the upper left panel where we loose the weekly periodicity. The upper right panel retains this periodicity and the predictions for the first days are relatively decent, but then we quickly under-predict the amplitude of the variations.

• The lower panels include two of the outliers from our time-series parameter space above; and here we see cases where things go really wrong. These kind of peculiar time series could lead to a bad performance for any otherwise decent forecasting algorithm if they contain a large enough fraction of visits in the test data set.

Overall, the results are not great, but given that it’s a fully automatic forecast (assuming only weekly periodicities) the auto.arima tool gives us a first baseline to compare other methods to.

For a more detailed exploration of ARIMA models take a look at this Kernel.

## Rank store to select the must important ones
ranked_store = air_visits.groupby('air_store_id', 
                observed=True)['visitors'].sum().sort_values(ascending=False)
                
# Create a 2x2 grid
fig = plt.figure(figsize=(8, 4))
gs = GridSpec(1, 2)

#Add plots to the grid
plot_auto_arima_air_id(air_id = "air_f3f9824b7d70c3cf",
                        ax = fig.add_subplot(gs[0, 0]))

plot_auto_arima_air_id(air_id = "air_8e4360a64dbd4c50",
                         ax= fig.add_subplot(gs[0, 1]))
# Adjust layout
plt.tight_layout()

# Show the plots
plt.show()

8.2 Prophet

The prophet forecasting tool is an open-source software developed by Facebook. It is available for both R and Python.

Prophet utilises an additive regression model which decomposes a time series into (i) a (piecewise) linear/logistic trend, (ii) a yearly seasonal component, (iii) a weekly seasonal component, and (iv) an optional list of important days (such as holidays, special events, …). It claims to be “robust to missing data, shifts in the trend, and large outliers”. Especially the missing data functionality could be useful in this competition

Let’s again explore the tool step by step. We will build on our work in the ARIMA section and won’t repeat any explanations that can be found there.

We will again create a training and validation set for the same periods as above (i.e before/after Mar 14th). The only differences to our ARIMA approach are that:

• We don’t need to replace NA values because prophet knows how to handle those.

• Prophet expects a data frame with two columns: ds for the dates and y for the time series variable.

air_id = "air_ba937bf13d40fb24"

pred_len <- test %>%
  separate(id, c("air", "store_id", "date"), sep = "_") %>%
  distinct(date) %>%
  nrow()

max_date <- max(air_visits$visit_date)
split_date <- max_date - pred_len
all_visits <- tibble(visit_date = seq(min(air_visits$visit_date), max(air_visits$visit_date), 1))

foo <- air_visits %>%
  filter(air_store_id == air_id)

visits <- foo %>%
  right_join(all_visits, by = "visit_date") %>%
  mutate(visitors = log1p(visitors)) %>%
  rownames_to_column() %>%
  select(y = visitors,
         ds = visit_date)

visits_train <- visits %>% filter(ds <= split_date)
visits_valid <- visits %>% filter(ds > split_date)

air_id = "air_ba937bf13d40fb24"

# Calculate prediction length
pred_len = test['id'].str.split('_', expand=True)[2].nunique()

# Find max date
max_date = air_visits['visit_date'].max()

# Calculate split date
split_date = max_date - timedelta(days=pred_len)

# Create a DataFrame with all visit dates
all_visits = pd.DataFrame({'visit_date': pd.date_range(start=air_visits['visit_date'].min(), end=max_date)})

# Filter air_visits for the specified air_id
foo = air_visits[air_visits['air_store_id'] == air_id]

# Merge with all_visits to ensure all dates are included
visits = all_visits.merge(foo, on='visit_date', how='left')

# Apply log transformation
visits['visitors'] = visits['visitors'].apply(lambda x: np.log1p(x))

# Split into train and validation sets
visits_train = visits[visits['visit_date'] <= split_date]
visits_valid = visits[visits['visit_date'] > split_date]

Here we fit the prophet model and make the forecast:

• the parameter changepoint.prior.scale adjusts the trend flexibility. Increasing this parameter makes the fit more flexible, but also increases the forecast uncertainties and makes it more likely to overfit to noise. The changepoints in the data are automatically detected unless being specified by hand using the changepoints argument (which we don’t do here).

• the parameter yearly.seasonality has to be enabled/disabled explicitely and allows prophet to notice large-scale cycles. We have barely a year of data here, which is definitely insufficient to find yearly cycles and probably not enough to identify variations on the time scales of months. Feel free to test the performance of this parameter.

proph <- prophet(visits_train, changepoint.prior.scale=0.5,
                yearly.seasonality=FALSE, daily.seasonality = FALSE)

## Error in prophet(visits_train, changepoint.prior.scale = 0.5, yearly.seasonality = FALSE, : could not find function "prophet"

future <- make_future_dataframe(proph, periods = pred_len)

## Error in make_future_dataframe(proph, periods = pred_len): could not find function "make_future_dataframe"

fcast <- predict(proph, future)

## Error in eval(expr, envir, enclos): object 'proph' not found

plot(proph, fcast)

## Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'proph' not found

from prophet import Prophet
from prophet.plot import plot

# Create a Prophet instance
proph = Prophet(changepoint_prior_scale=0.5,
                yearly_seasonality=False,
                daily_seasonality=False)

# Prepare the DataFrame
visits_train = visits_train.rename(columns={'visit_date': 'ds', 'visitors': 'y'})

# Fit the model
proph.fit(visits_train)

## <prophet.forecaster.Prophet object at 0x7f7efb72ac50>
## 
## 13:08:26 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:26 - cmdstanpy - INFO - Chain [1] done processing

# Create a DataFrame for future dates
future = proph.make_future_dataframe(periods=pred_len)

# Generate forecasts
fcast = proph.predict(future)

fcast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()

##             ds      yhat  yhat_lower  yhat_upper
## 389 2017-04-18  2.619568    2.046414    3.141031
## 390 2017-04-19  2.874313    2.334234    3.410974
## 391 2017-04-20  2.671990    2.147631    3.197199
## 392 2017-04-21  3.216012    2.674706    3.758543
## 393 2017-04-22  2.995465    2.452739    3.510706

plt.style.use('ggplot')
#fig = proph.plot(fcast)

# Plot the value with line and scatter
#plt.plot(fcast['ds'], fcast['yhat'], label='Value', color='red')
p= plt.scatter(fcast['ds'], fcast['yhat'], color='black', alpha=0.5, s =3)

# Plot the confidence intervals
p= plt.fill_between(fcast['ds'], 
                    fcast['yhat_lower'], fcast['yhat_upper'], 
                    color='blue', alpha=0.05) #, label='Confidence Interval'

# Add labels and legend
p= plt.xlabel('Date')
p= plt.ylabel('Value')
#plt.legend()

# Show the plot
plt.show(p)

The observed data are plotted as black points and the fitted model, plus forecast, as a blue line. In light blue we see the corresponding uncertainties.

Prophet offers a decomposition plot, where we can inspect the additive components of the model: trend, yearly seasonality (if included), and weekly cycles:

prophet_plot_components(proph, fcast)

## Error in prophet_plot_components(proph, fcast): could not find function "prophet_plot_components"

from prophet.plot import plot_components
# Generate the components plot
#fig = plot_components(proph, fcast)

# Create a 2x2 grid
fig = plt.figure(figsize=(6, 4))
gs = GridSpec(2, 1)

ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[1, 0])

p= ax1.plot(fcast['ds'], fcast['trend'], color = 'blue')
p= ax1.set_xlabel('date', fontsize=6)
p= ax1.set_ylabel('Trend', fontsize=6)
p= ax1.tick_params(axis='x', rotation=10, labelsize= 7) 

fcast['ds'] = pd.to_datetime(fcast['ds'])
fcast['weekday'] = fcast['ds'].dt.day_name()
weekly = fcast.groupby(['weekday'])['weekly'].mean().reindex(['Sunday',
         'Monday','Tuesday','Wednesday','Thursday','Friday','Saturday'])

p= ax2.plot(weekly, color = 'blue')
p= ax2.set_xlabel('date', fontsize=6)
p= ax2.set_ylabel('Weekly', fontsize=6)
p= ax2.tick_params(axis='x', rotation=10, labelsize= 7)

# Adjust layout
plt.tight_layout(p)

## tight_layout() takes 0 positional arguments but 1 was given

plt.show(p)

We find:

• Prophet detects a weekly variation pattern which is similar to what we had found before, in that Fri/Sat are more popular than the rest of the week. The difference, however, is that here Sun has a very low average visitor count. This might be be due to the properties of this particular restaurant, a “Dining Bar” in “Tokyo”. In Fig. 23 we see that “Dining Bars” in general are not as busy on Sundays; although not to such a large extent as we see in this graph. The difference in visitors on Sat vs Sun might be an interesting feature of an eventual model.

• The long-term trend is different from the average behaviors displayed in Fig. 11, which were more likely to rise toward the end of 2016. Here we see a peak in mid 2016.

• Note, that this is one specific time series. I’ve checked other time series as well and many of them showed the expected Fri/Sat/Sun vs Mon-Thu variations along with a long-term peak around Dec 2017. Feel free to fork this Kernel and check for yourself.

So: This is a good start, but we will of course use our trusted ggplot2 to give us more control over the plotting parameters:

fcast %>%
  as.tibble() %>%
  mutate(ds = date(ds)) %>%
  ggplot(aes(ds, yhat)) + 
  geom_ribbon(aes(x = ds, ymin = yhat_lower, ymax = yhat_upper), fill = "light blue") +
  geom_line(colour = "blue") +
  geom_line(data = visits_train, aes(ds, y), colour = "black") +
  geom_line(data = visits_valid, aes(ds, y), colour = "grey50")

## Warning: `as.tibble()` was deprecated in tibble 2.0.0.
## ℹ Please use `as_tibble()` instead.
## ℹ The signature and semantics have changed, see `?as_tibble`.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Error in eval(expr, envir, enclos): object 'fcast' not found

That doesn’t look too bad. We plot our training visitor counts in black, the validation set in grey, and the forecast plus uncertainties in blue and light blue, again.

# Convert 'ds' column to datetime
fcast['ds'] = pd.to_datetime(fcast['ds'])

# Plotting
p= plt.figure(figsize=(10, 6))

# Forecast line
p= plt.plot(fcast['ds'], fcast['yhat'], color='blue', label='Forecast')

# Confidence interval ribbon
p= plt.fill_between(fcast['ds'], fcast['yhat_lower'], fcast['yhat_upper'], 
                    color='lightblue', alpha=0.5)

# Training data
p= plt.plot(visits_train['ds'], visits_train['y'], 
            color='black', label='Training Data')

# Validation data
p= plt.plot(visits_valid['visit_date'], visits_valid['visitors'],
            color='grey', label='Validation Data')

# Add labels and title
p= plt.xlabel('Date')
p= plt.ylabel('yhat')
p= plt.title('Prophet Forecast with Confidence Intervals')

# Add legend
p= plt.legend()

# Show the plot
plt.show(p)

Let’s turn this into another function:

plot_prophet_air_id <- function(air_id){
  
  pred_len <- test %>%
    separate(id, c("air", "store_id", "date"), sep = "_") %>%
    distinct(date) %>%
    nrow()

  max_date <- max(air_visits$visit_date)
  split_date <- max_date - pred_len
  all_visits <- tibble(visit_date = seq(min(air_visits$visit_date), 
                                        max(air_visits$visit_date), 1))

  foo <- air_visits %>%
    filter(air_store_id == air_id)

  visits <- foo %>%
    right_join(all_visits, by = "visit_date") %>%
    mutate(visitors = log1p(visitors)) %>%
    rownames_to_column() %>%
    select(y = visitors,
          ds = visit_date)

  visits_train <- visits %>% filter(ds <= split_date)
  visits_valid <- visits %>% filter(ds > split_date)
  
  proph <- prophet(visits_train, changepoint.prior.scale=0.5,
                   yearly.seasonality=FALSE, 
                   daily.seasonality = FALSE)
  future <- make_future_dataframe(proph, periods = pred_len)
  fcast <- predict(proph, future)
  
  p <- fcast %>%
    as.tibble() %>%
    mutate(ds = date(ds)) %>%
    ggplot(aes(ds, yhat)) +
    geom_ribbon(aes(x = ds, ymin = yhat_lower, 
                    ymax = yhat_upper), fill = "light blue") +
    geom_line(colour = "blue") +
    geom_line(data = visits_train, aes(ds, y), colour = "black") +
    geom_line(data = visits_valid, aes(ds, y), colour = "grey50") +
    labs(title = str_c("Prophet for ", air_id))
  
  return(p)
}  

def plot_prophet_air_id(air_id, ax):
  
  # Separate the 'id' column into three columns
    test[['air', 'store_id', 'date']] = test['id'].str.split('_', expand=True)
  # Get distinct dates and calculate the number of rows
    pred_len = test['date'].nunique()
    # Find the maximum visit date
    max_date = pd.to_datetime(air_visits['visit_date'].max())

    # Calculate the split date
    split_date = max_date - timedelta(days=pred_len)

    # Create a DataFrame with a sequence of dates
    all_visits = pd.DataFrame(
      {'visit_date': pd.date_range(start=min(air_visits['visit_date']),
                                  end=max(air_visits['visit_date']))}
    )
    
    # Filter air_visits for the specified air_id
    foo = air_visits[air_visits['air_store_id'] == air_id]

    foo['visit_date'] = pd.to_datetime(foo['visit_date'])
     
    # Merge with all_visits to ensure all dates are included
    visits = all_visits.merge(foo, on='visit_date', how='left')

    # Apply log transformation
    visits['visitors'] = visits['visitors'].apply(lambda x: np.log1p(x))
    visits['y'] = visits['visitors']
    visits['ds'] = visits['visit_date']
    #visits = visits[["ds", "y"]]

    # Split into train and validation sets
    visits_train = visits[visits['ds'] <= split_date]
    visits_valid = visits[visits['ds'] > split_date]
    
    # Create a Prophet instance
    proph = Prophet(changepoint_prior_scale=0.5,
                yearly_seasonality=False,
                daily_seasonality=False)
    # Fit the model
    proph.fit(visits_train)

    # Create a DataFrame for future dates
    future = proph.make_future_dataframe(periods=pred_len)

    # Generate forecasts
    fcast = proph.predict(future)
    
    # Convert 'ds' column to datetime
    fcast['ds'] = pd.to_datetime(fcast['ds'])

    # set plot
    fig, ax = plt.subplots(figsize=(4, 4))
    plt.style.use('ggplot')

    # Confidence interval ribbon
    ax.fill_between(fcast['ds'], fcast['yhat_lower'], 
                    fcast['yhat_upper'], color='lightblue',
                    alpha=0.5)

    # Forecast line
    ax.plot(fcast['ds'], fcast['yhat'], 
            color='blue', label='Forecast')

    # Training data
    ax.plot(visits_train['ds'], visits_train['y'], 
           color='black', label='Training Data')

    # Validation data
    ax.plot(visits_valid['visit_date'], visits_valid['visitors'],
            color='grey', label='Validation Data')

    # Add labels and title
    ax.tick_params(axis='x', rotation=10, labelsize= 7)
    plt.xlabel('Date')
    plt.ylabel('yhat')
    

p1 <- plot_prophet_air_id("air_f3f9824b7d70c3cf")

## Error in prophet(visits_train, changepoint.prior.scale = 0.5, yearly.seasonality = FALSE, : could not find function "prophet"

p2 <- plot_prophet_air_id("air_8e4360a64dbd4c50")

## Error in prophet(visits_train, changepoint.prior.scale = 0.5, yearly.seasonality = FALSE, : could not find function "prophet"

p3 <- plot_prophet_air_id("air_1c0b150f9e696a5f")

## Error in prophet(visits_train, changepoint.prior.scale = 0.5, yearly.seasonality = FALSE, : could not find function "prophet"

p4 <- plot_prophet_air_id("air_820d1919cbecaa0a")

## Error in prophet(visits_train, changepoint.prior.scale = 0.5, yearly.seasonality = FALSE, : could not find function "prophet"

layout <- matrix(c(1,2,3,4),2,2,byrow=TRUE)
multiplot(p1, p2, p3, p4, layout=layout)

That looks not bad either. Looks like we’re overestimating the trend component, which could probably use less flexibility, for at least three of these. The forth time series has too little data for prophet to be able to do much. Here we could discard the trend component completely or simply take the median.

# Create a 2x2 grid
fig = plt.figure(figsize=(12, 4))
gs = GridSpec(2, 2)

#Add plots to the grid
p= plot_prophet_air_id(air_id = "air_f3f9824b7d70c3cf", 
                        ax = fig.add_subplot(gs[0, 0]))

## 13:08:37 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:37 - cmdstanpy - INFO - Chain [1] done processing

p= plot_prophet_air_id(air_id = "air_8e4360a64dbd4c50", 
                         ax= fig.add_subplot(gs[0, 1]))

## 13:08:38 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:38 - cmdstanpy - INFO - Chain [1] done processing

                         
p= plot_prophet_air_id(air_id = "air_1c0b150f9e696a5f",
                         ax= fig.add_subplot(gs[1, 0]))

## 13:08:40 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:40 - cmdstanpy - INFO - Chain [1] done processing

                         
p= plot_prophet_air_id(air_id = "air_820d1919cbecaa0a",
                         ax= fig.add_subplot(gs[1, 1]))                         

## 13:08:41 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:41 - cmdstanpy - INFO - Chain [1] done processing

                         
plt.show(p)

Remember that prophet also gives us the possibility to include holidays and other special events in our forecast. For our task, this could be very useful in taking the Golden Week into account. For more insights from a tailored analysis of the Golden Week’s impact have a look at this kernel.

Since the holiday data is readily available in this competition we only need to rename it according to prophet’s liking to include it in our forecast function. Let’s modify that function see whether holidays make a difference when predicting for the 2016 Golden Week. The only thing we need to do is to truncate our air_visits data on May 31 2016 in an intermediate step:

plot_prophet_air_id_holiday <- function(air_id, use_hday){
  
  air_visits_cut <- air_visits %>%
    filter(visit_date <= ymd("20160531"))
  
  hday <- holidays %>%
    filter(holiday_flg == TRUE) %>%
    mutate(holiday = "holiday") %>%
    select(ds = date, holiday)
  
  pred_len <- test %>%
    separate(id, c("air", "store_id", "date"), sep = "_") %>%
    distinct(date) %>%
    nrow()

  max_date <- max(air_visits_cut$visit_date)
  split_date <- max_date - pred_len
  all_visits <- tibble(visit_date = seq(min(air_visits_cut$visit_date), max(air_visits_cut$visit_date), 1))

  foo <- air_visits_cut %>%
    filter(air_store_id == air_id)

  visits <- foo %>%
    right_join(all_visits, by = "visit_date") %>%
    mutate(visitors = log1p(visitors)) %>%
    rownames_to_column() %>%
    select(y = visitors,
          ds = visit_date)

  visits_train <- visits %>% filter(ds <= split_date)
  visits_valid <- visits %>% filter(ds > split_date)
  
  if (use_hday == TRUE){
    proph <- prophet(visits_train,
                     changepoint.prior.scale=0.5,
                     yearly.seasonality=FALSE,
                     daily.seasonality=FALSE,
                     holidays = hday)
    ptitle = "Prophet (w/ holidays) for "
  } else {
     proph <- prophet(visits_train,
                     changepoint.prior.scale=0.5,
                     yearly.seasonality=FALSE,
                     daily.seasonality = FALSE)
    ptitle = "Prophet for "
  }
  
  future <- make_future_dataframe(proph, periods = pred_len)
  fcast <- predict(proph, future)
  
  p <- fcast %>%
    as.tibble() %>%
    mutate(ds = date(ds)) %>%
    ggplot(aes(ds, yhat)) +
    geom_ribbon(aes(x = ds, ymin = yhat_lower, ymax = yhat_upper), fill = "light blue") +
    geom_line(colour = "blue") +
    geom_line(data = visits_train, aes(ds, y), colour = "black") +
    geom_line(data = visits_valid, aes(ds, y), colour = "grey50") +
    labs(title = str_c(ptitle, air_id))
  
  return(p)
}  

def plot_prophet_air_id_holida(air_id, use_hday ,ax):
  
  # Separate the 'id' column into three columns
    test[['air', 'store_id', 'date']] = test['id'].str.split('_', expand=True)
  # Get distinct dates and calculate the number of rows
    pred_len = test['date'].nunique()
    # Find the maximum visit date
    max_date = pd.to_datetime(air_visits['visit_date'].max())

    # Calculate the split date
    split_date = max_date - timedelta(days=pred_len)

    # Create a DataFrame with a sequence of dates
    all_visits = pd.DataFrame({'visit_date': pd.date_range(start=min(air_visits['visit_date']),
    end=max(air_visits['visit_date']))})
    
    # Filter air_visits for the specified air_id
    foo = air_visits[air_visits['air_store_id'] == air_id]

    # Merge with all_visits to ensure all dates are included
    visits = all_visits.merge(foo, on='visit_date', how='left')

    # Apply log transformation
    visits['visitors'] = visits['visitors'].apply(lambda x: np.log1p(x))
    visits['y'] = visits['visitors']
    visits['ds'] = visits['visit_date']
    #visits = visits[["ds", "y"]]

    # Split into train and validation sets
    visits_train = visits[visits['ds'] <= split_date]
    visits_valid = visits[visits['ds'] > split_date]
    
    if use_hday == True:
      # Create a Prophet instance
      proph = Prophet(changepoint_prior_scale=0.5,
                yearly_seasonality=False,
                daily_seasonality=False)      
      # Add holidays
      proph.add_country_holidays(country_name='JP')
      ptitle = "Prophet (w/ holidays) for "

    else:
        # Create a Prophet instance
      proph = Prophet(changepoint_prior_scale=0.5,
                yearly_seasonality=False,
                daily_seasonality=False)
      ptitle = "Prophet for"
      
    # Fit the model
    proph.fit(visits_train)

    # Create a DataFrame for future dates
    future = proph.make_future_dataframe(periods=pred_len)

    # Generate forecasts
    fcast = proph.predict(future)
    
    # Convert 'ds' column to datetime
    fcast['ds'] = pd.to_datetime(fcast['ds'])

    # set plot
    fig, ax = plt.subplots(figsize=(8, 4))
    plt.style.use('ggplot')

    # Confidence interval ribbon
    ax.fill_between(fcast['ds'], fcast['yhat_lower'], 
                    fcast['yhat_upper'], color='lightblue',
                    alpha=0.5)

    # Forecast line
    ax.plot(fcast['ds'], fcast['yhat'], 
            color='blue', label='Forecast')

    # Training data
    ax.plot(visits_train['ds'], visits_train['y'], 
           color='black', label='Training Data')

    # Validation data
    ax.plot(visits_valid['visit_date'], visits_valid['visitors'],
            color='grey', label='Validation Data')

    # Add labels and title
    ax.tick_params(axis='x', rotation=10, labelsize= 7)
    plt.xlabel('Date')
    plt.ylabel('yhat')
    plt.title('use_hday: '+ str(use_hday))
 

# Create a 2x2 grid
fig = plt.figure(figsize=(12, 4))
gs = GridSpec(2, 1)

#Add plots to the grid
p= plot_prophet_air_id_holida(air_id = "air_f3f9824b7d70c3cf", use_hday=True,
                        ax = fig.add_subplot(gs[0]))

## 13:08:45 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:45 - cmdstanpy - INFO - Chain [1] done processing

p= plot_prophet_air_id_holida(air_id = "air_f3f9824b7d70c3cf", use_hday=False,
                         ax= fig.add_subplot(gs[1]))

## 13:08:47 - cmdstanpy - INFO - Chain [1] start processing
## 13:08:47 - cmdstanpy - INFO - Chain [1] done processing

                         
plt.show(p)

# 
# playoffs = pd.DataFrame({
#   'holiday': 'playoff',
#   'ds': pd.to_datetime(['2008-01-13', '2009-01-03', '2010-01-16',
#                         '2010-01-24', '2010-02-07', '2011-01-08',
#                         '2013-01-12', '2014-01-12', '2014-01-19',
#                         '2014-02-02', '2015-01-11', '2016-01-17',
#                         '2016-01-24', '2016-02-07']),
#   'lower_window': 0,
#   'upper_window': 1,
# })
# superbowls = pd.DataFrame({
#   'holiday': 'superbowl',
#   'ds': pd.to_datetime(['2010-02-07', '2014-02-02', '2016-02-07']),
#   'lower_window': 0,
#   'upper_window': 1,
# })
# holidays_example = pd.concat((playoffs, superbowls))
# 
# holidays_example.tail

# m = Prophet(changepoint_prior_scale=0.5, yearly_seasonality=False, daily_seasonality=False)
# 
# # Add holidays
# m.add_country_holidays(country_name='US')